Unplug the power cord from the computer. Look at the back and keep your eye on the fan. Plug in the power cord. Did the fan move at all? Next, attempt to turn on the computer while looking again at the fan. Did the fan attempt to spin when you tried to turn it on?
Next, open the case. While it is plugged in, but not on, do you see a glowing LED on the logic board? Watch the logic board and try to turn the computer on. Does anything on the board light up for even a second? Check that the cables from the power supply are connected snug to the logic board and try starting it again.
If you do all this and see no signs of life, then either the power supply or the logic board are bad. On such an old machine, finding a replacement part isn't going to be worth it.