No way if you are buying new parts. Not sure how much used parts go for.

Here you go!

DVD Drive:
http://www.newegg.com/Product/Product.aspx?Item=N82E16827106289

Hard Drive:
http://www.newegg.com/Product/Product.aspx?Item=N82E16822136769

Motherboard:
http://www.newegg.com/Product/Product.aspx?Item=N82E16813128664

Power Supply:
http://www.newegg.com/Product/Product.aspx?Item=N82E16817139020

Ram:
http://www.newegg.com/Product/Product.aspx?Item=9SIA0ST0DV4434

CPU:
http://www.newegg.com/Product/Product.aspx?Item=N82E16819113349

GPU:
http://www.newegg.com/Product/Product.aspx?Item=N82E16814150642

Total: $514. - With about $50 worth of rebates you can claim.

What you get:
3.7-3.9ghz Quad Core CPU.
8Gb DDR3.
Radeon 7850 with room on the motherboard and extra overhead on the Powersupply to add a second Radeon 7850 down the line.
Although, personally a Radeon 7870 or R9 270 would be better, such as this: http://www.newegg.com/Product/Product.aspx?Item=N82E16814161452
(You can crossfire the 7870 and 270.)

I would also opt for a Cooler Master Hyper 212+ for the CPU so you can overclock it, you will also be able to upgrade to Steamroller in the future and possibly the CPU that comes after that.

Won't be true for much longer.

LMAO the cpu on a PS4 and the Xbone for that matter is not optimized for games.... LMAO its basically 2 slow quad core cpus designed for a tablet lumped together. Hardly what you would call Gaming optimized.

Im not saying that games will look bad on consoles but ignorant statements like this really shouldnt be propogated. 

BULLSHIT. the CPU is not some magical beast optimised for gaming at all. That is the easiest item to outperform with a relativley cheap quad core i5. You also don't have 8GB GDDR5 allocated to the GPU, it is a unified memory model so that OS has to live in and use that RAM too. 8GB DDR3 + a decent GPU with 2-3GB DEDICATED of GDDR5 will comfortably outperform it.

Without monitor, keyboard etc you should be able to beat performance with budget parts. Add little more though and you can completely blitz it.

You don't even need a Core i5.

Jaguar is around 10-20% faster than Brazos per core, with 8 cores it would be equivalent to roughly a Dual-Core Hyper-threaded Haswell Core i3.
The reason why PC's have historically required faster CPU's than the console equivalent is because of draw cells, which are soon to be essentially a thing of the past.

Also something to keep in mind is that even AMD's fastest CPU's pale in comparison to even some of Intel's slowest, even with twice the cores in AMD's favour.
Besides the Playstation 4 and Xbox One don't allow for all 8 anemic cores to be used for gaming anyway.

Jaguar is a 2 issue, low clocked, low IPC, small caches (No, L3) with pretty poor Floating Point and Integer units.
It's a budget processor which is designed to be "good enough" not class leading, Microsoft and Sony spent all their transister budgets on the GPU and other subsystems, not the CPU.
If Microsoft and Sony wanted decent CPU performance, they would have to pay for it which is not ideal in a cost sensitive device, which means higher cost consoles for all the consumers who would have then complained untill the cows came home.

(Forget about it.)

Sorry, but you are wrong here. The unified memory in this case improves vastly the performance. People think its bad because of onboard video cards. A PC onboard video card shares DDR3 memory with the CPU. That is worse than having DDR3 for CPU and GDDR5 for the GPU. But on PS4 there is a unified GDDR5 architecture. That means that the CPU and the GPU can share data for free. You can run heavy physics operation on the GPU easily without passing by a slow PCI Express interface. While the GPU on PS4 can access data that is being used by the CPU at 176GB/s, a regular PC would have to pass it for the PCI Express interface (15GB/s in version 3.0). That is a massive performance impact that some timestimes actually makes developer do a calculation that would be faster on the GPU using the CPU only because of it. So it won't outperform the PS4 architecture, it will actually be underperforming by a significant margin.

I'm gonna put another interesting data. CPU. If you grab a more powerful CPU, even a 16-core one, it won't help you that much. At some years, we had nice single core CPUs using the main memory. Now we have 8 or 16 CPUs using the same memory and splitting bandwidth. The number of cores and general CPU speed improves much faster than the memory bandwidth (its called the "memory wall") and it only will got worse. PS4 has a good advantage for using 8 cores with very fast memory. We are in a point in tech that throwing horsepower can, by the first time in computing history, only make things worse. Software optimization is what will have to drive things forward.

lol me owinign a i7 2600k and he tells me that!!!

if anything PS4 has a good GPU and GDDR5 RAM which has its cons and pros

Your entire first part of the argument is that the CPU is powerfull because the GPU can assist in processing.
Well here is a news flash. - The PC can do it too, in-fact it's been doing it longer than the consoles, but that doesn't actually make the CPU powerfull, that just means the CPU is weak and is getting assistance from another processor.
In the PC space they do it to conserve energy.

And another fact is, Ram is a temporary fast form of storage, it DOES NOT do any form of processing, you could have 1024GB/s of memory bandwidth, but if you don't have the compute resources to make any use of it... Then it would be utterly and completely pointless.
Besides the PS4's memory bandwidth has to be split between the CPU, GPU and what-ever other processors the PS4 uses, that 176GB/s number? It's going to be much lower than that for actuall games.
You basically took the number Sony advertised and ran with it, claiming it as the holy grail, the reality is far different that that I'm afraid.
The same thing occured with the Playstation 3 and the pretty horrible performing Cell.

As for PCI-E's bandwidth, especially PCI-E 3.0 16x isn't a problem, not even really for compute, there is a reason why there is GDDR5 Memory next to the GPU so that the PCI-E interface isn't hammered hard and constantly, but that's simple logic.
Besides, the GDDR5 Ram in my PC is faster than the PS4's, the PC will also move to GDDR6 and/or maybe XDR2 Ram soon, possibly within the next GPU release cycle.
You also have 512bit memory configurations in the PC rather than the mid-range 256bit bus the PS4 employs.

As for the memory wall, that has to be the funniest thing I have read all day.
So what you're saying is that you would see no difference in performance moving from a Core i3 (Which is essentially how fast an 8 core Jaguar would be.) to a Core i7 6-core, 12 threaded processor if you used the same Ram.
I have the ability to disable my cores and hyper threads, wan't me to disable them more to represent a Dual-Core? I can assure you the performance gains are real and stupidly massive by having all functional units enabled.

I also have a Phenom 2 x6 1090T 6 core processor in another PC and the motherboard supports DDR2 and DDR3 Ram, the CPU also has a DDR2 and DDR3 memory controller, wan't to know what I discovered a few years back? There was ZERO and I mean ZERO differences in performance between DDR2 800mhz Ram and DDR3 1866mhz Ram in gaming on the PC.

CPU's have Caches to keep data that's required for processing near the compute engines, which is both stupidly fast and low latency.
The CPU also utilises various types of predictors so that it can predict the data it is going to require ahead of time, this prevents a resource stall where if the CPU doesn't have the data it needs in the Cache it has to travel all the way down to system memory and regardless of how fast or low latency the system memory is, it will NEVER make up for the bandwidth and latency differences between the L4/L3/L2 and L1 caches.
Simple fact of the matter is, Jaguar's predictors are relatively simple, it's going to be doing allot of slow trips down to the GDDR5 Ram, possibly wasting millions/billions of cycles.

This may also hurt your pride for the Playstation 4 a bit, but... Without the PC and the PC's technology that PC's gamers have essentially "Funded" the research and development for... You wouldn't have the Playstation 4 at all, not how it is today.
You would more than likely ended up with an ARM based solution that a mobile phone uses instead.

You might want to check out GPU prices again.  I see 4 GB GDDR5 GPU's for $250 on Newegg.

Besides, GDDR5 is not very good for general purpose computing making it uneccesary for a computer to have the entire RAM pool based on GDDR5 (which, by the way, is actually DDR3 with some tweaks).