If you were to be a little more specific as to why it's not working; you'd be a lot more successful.
However, check that the console is plugged into power, in both the wall, and at the Playstation itself.
If you find that when you try to turn it on it sounds like it's on, but the T.V doesn't pick it up, you may have possibly forgotten to plug in the display cables, or have mixed them up somehow.
No PlayStation 3 games do NOT work on the PlayStation 2 system.
No they do not work in a PS2
no
No.
The original Sony 8MB memory cards (for PlayStation 2) work best, but any memory card will work in the PlayStation 2 Slim
yes
Yes.
No.
no
Yes they can.
no, but you can play playstation 1 games on a ps2
If it is a playstation 3 and the TV has HDMI input and you have a HDMI calbe then it will work.