I had the same problem. Uncharted 3 wouldn't work, neither would Blu-Ray movies, it got to the point to where almost nothing would ever work, except DVDs. There seem to be 3 solutions. Buy a new PS3, buy a new disc drive, or send it into Sony.
I bought a new PS3.
A new disk drive is easy to replace
But not cheap.
At least not from my experience. I had the fat 80GB (original with 4 USB ports) and my Blu Ray Drive went out about a month after warranty expired and it was going to cost $160 to replace. I just bought a slim instead.
So every other game works with your PS3, just not your new TLoU?
If this is the case, I would first exchange your copy of TLoU for a new one from the retailer you bought it from.
If the replacement still will not work with your PS3, then I would replace the blu-ray lens of your drive. They can be had for about $20 to $30. If you are not confident that you can replace the lens, then replace the drive as discussed above.
If a PS3 game doesn't work in a PS3, its not your responsibility to pay for a fix.
If your console is no longer covered by warranty, then yeah, you have to pay for a fix... it sucks, but that's how it is.
That's why I advise some people to buy it from the PS store instead.