How can you tell if a backup is patched?

Using CDRWin to read the first sectors there ought to be an indication of who patched the game writtien into the part that normally displays PLAYSTATION2. But not everyone follows the rules when making a patch for a game so it might not be possible without comparing the original with the copy (Difficult if it's a rip!).

The other convention to be followed when selling backup games (illegal and I don't sell/buy these) is that they are patched to work. So at worst you may have to add a patch for, say, playing a PAL game on an NTSC TV. That's not straightforward if you don't know the original game version in case the patch is a mismatch. Then you have to use NOTEPAD.EXE to read the SYSTEM or STSTEM.CNF file which will tell you whether the game is PAL or NTSC. It won't tell you if the game has been patched, but generally PAL/NTSC patches are not previously applied by game sellers.

Finally, if the game doesn't boot at all on a chipped (8 wire mod) PS2, there could be two reasons:

1 The copier person didn't include a needed fix (unlikely but possible)
2 The media is in unreadable condition for the PS2

Hope that helps.