Instructions
Verify that you really have a genuine PlayStation 2. Since an original PlayStation resembles a PS2 in some features, you should look at the back of the console to verify the name.
Reset your PlayStation 2 in one of two ways: Unplug the power cord from the outlets or by turn the power on the console off and back on. This should fix any electrical problems that may occur with the game console.
Check game discs to make sure that no scratches or dents exist. Look for signs of a defect on your PS2 game or lack thereof on your PS1 game. This could help explain why your PS2 game does not work while your PS1 does.
Call Sony with your problem. You will receive help either by sending in your system for repair or have your console replaced if it is under warranty.