I don't think there's gonna be backwards compatibility built into PS4s, so you'd have to pick up a PS4 copy.
Some places are doing reduced price trade ups on certain games I think but I don't know the details off the top of my head.
Re: Off Top: Broken PS3 Advice
Sounds like the bluray drive might be knackered. Quite common with old 'fat' models, not so sure about the new ones.
If you're reasonably tech savvy it is something you might be able to replace yourself but in all honestly you're best going to Sony for a swap...