My PS3 does not recognise when a game is inserted, I therefore can't start a game.

Hmm. May be because the disc is scratched? Not sure what it would be otherwise, if other games work just fine.

u try ugrading your ps3 and try to make it read your dvd since it might be a upgraded verstion of game..in som cases the original dvd wil only be recognised in that u make sure whether its original or not..still u truck with it check this to solve

Hmmm mayby wash the disc and dry it CARFULLY and if you PS3 stands up it has a harder time playing games...

swich back and forth between the ps2 game and ps3 game or just keep putting in the ps3 game until it reads it. your laser is probally going.

Hi, the problem you have is the ps3 laser head is faulty or dirty making it unable to read games or discs, you may need to get this repaird or if under warrenty get a repaclement.

take some alchol and a couple of swabs and put some alchol on the swab and clean out the disk tray but dont stick it in to 2 far take it out once u fill a little pressure.

PS3 is The amazing device by sony but it has some common problems like unreadable disc, disc error etc.... Good news is that these all problems can be repaired with the help of DIY Guides, one such guide available at PS3 Repair Blog
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Sounds like it could be failure of the Blu-ray drive. A friend of mine had the same issue.

Contact Sony support and if it's under warranty they will fix it free of charge (here in Australia they do anyway).

Actually only 60GB PS3s supports PS2 games. But It requires particular firmware. In first instance try updating your system, then dissable the disc autoload function, insert PS2 game, and look at the game section if your soft will recognise it. If yes just try to play

Good luck

Ring Sony, and they will replace your machine if its still in warranty.