If your system isn't reading it, I would say that you probably can't play it. Only a few of the models from the original release of the system is fully backwards compatible. The majority of the systems will only play PS1 games as far as previous systems' games. Sorry, but you can still buy PS2s and for very cheap.
You would need to find a stock 20GB or 60GB older-model PS3 to properly run PS2 games. Those older-models had the hardware-based emulation VIA the Emotion Engine and could run most games pretty flawlessly. I've never had a problem, and I've got a 20GB upgraded to a 250GB (yay laptop drives!)
also if you do have a model thats compatible to run the ps2 games you will need to login threw your online account and download a the backwards compatible file and install it...google this its all over the internet
PS3 is worlds ahead of it's predecessor. Internal HD means no more memory cards to save game data. Blu Ray readability means it doubles as your Blu Ray player. Online game play/updates is also a plus. Plus you can surf the web (assuming you have wireless internet). I really dig the wireless controllers (though I DON"T dig the $60 price tag for an extra one).
While I still play my PS2 I have to mention the graphics on my Gran Turismo games have such a phenomenal difference between the consoles. What I thought was state of the art 9 years ago looks like outdated Atari games today.
My son is drop dead addicted to Call of Duty. Any version.