Okay so heres my situation.

Last year when I was playing Skyrim, my PS3 broke down and failed to turn back on. I had a 320GB HDD inside that was one i bought, mine originally came with the 80GB. So I made arrangements to send it back to Sony to have it fixed, but also went out and bought a new PS3. I swapped the 80GB HDD back in and kept my 320 since it had a ton of movies and music on it. i bought the 120GB slim and i got my old Phat back with the 80GB HDD. So now i have 2 PS3 3 HDDs and an external case for it.

I tried to backup the files to the computer like i did when my first PS3 broke but I cannot seem to manager to do that.

I tried using the two PS3s but when I put in my 320GB HDD it says I need to format the system, which would erase my data, but I'm confused since it should already be in the PS3's format. 

I can retry these methods with some advice from someone that has done it before, or if someone would have a different method that would be greatly appreciated. 

you will always have to reformat the hard drive whne you put it in the ps3 so you have the sky rim on the 320 gig thats out of the ps3 you cant transfer to a usb stick??

As soon as you take out the harddrive you have to automatically reformat it when putting it back in, if you didn't backup any of the info of the HDD that's currently out of the PS3 then I'm sorry you probably just lost everything. I'm not sure if there is a way to back it all up on PC or not, there may be a way now.

Correct, I cannot transfer any files from the 320GB HDD to any type of device, I can't even get my computer to recognize the HDD.

The PS3 i received back was the same one i sent to them, as it also had my Skyrim game still in it. I tried swap the HDD back in before i turned it back on but it still didn't work..

When i called Sony to set up the repair, they were the ones who told me to replace my old on back in to avoid my data being erased..

Okay so here's my thought.. could I download the update data that my old HDD is on, put that on a USB, put my HDD back in and try to see if that allows me to run my HDD on my PS3 again? or wouldn't that work?

When I got a 500 GB hard drive to replace my 160, the only thing that worked was putting all my save data on a flash drive/online storage, and downloading ALL the games, updates, and all that stuff all over again. As long as you still have your save data, it isn't too big of a burden.

Well I was a PS+ member before it happened so some games saves were.. well saved. but I'm more upset about losing all the movies I lost on PSN and all the songs I had on there as i didn't have a computer and the PS3 was basically my storage container. Also i miss my rockband stuff again. i ha over 300 songs from DLC ( mostly my friends) but now that they changed game sharing i can't get on his.

I am able to get my computer to finally recognize that there is a device now, however it also asks to reformat in order to use it, it won't let me open it or anything.