Hi,

Does the PS3 40Gb pack have a HDMI-cable right out of the box? 

Nope.

Well that sucks, how much do they cost?

sadly no , but don't get fooled into buying a super-expensive cable - a normal 10€ cable has the same picture quality

I paid $25 for a reliable brand one with lifetime warranty. Don't buy those monster type ones that go for over $100.

I think my official Nintendo component cables were $50 AUD.

Nope unfortunately. I got my HDMI cable with lifetime warranty for just over $100 Australian dollars
(90US).

why would you need a lifetime warranty for a cable anyway ? if it's damaged after 2-3 years you can simply pick up a new one for 3-5€ (with time they become less expensive)

nope, but thankfully my xbox elite came with one, so i just use my xbox one with my ps3

There's a myth about HDMI that the more expensive cables are helpful. This is not the case however that is a bit deceiving. After a certain distance cable quality will matter but for short distances (6' or 6m and under) the cheap cables will work just about the same as more expensive cables. I have a 3m cable I paid 2$US for with shipping and it works as well as the other cables I own.

So long as the HDMI has good connectors, the wire is shielded and there's no breaks in it at short distances it will be just fine so but a cheap one for your PS3 unless for some weird reason you want it 30'(30m) away from the TV but I don't really see that happening..