Clear the CMOS and try the P3 again. To clear the CMOS, you can either find the CLEAR CMOS jumper and with the system unplugged from the wall outlet set the jumper to the CLEAR position for 5 minutes. Then reset the jumper to the NORMAL position, plug the system back in and boot it up.
Or you can unplug the system from the wall outlet and remove the motherboard battery for 5 minutes. Since that system is pretty old, replace the battery with a new one. Plug the system back into the wall outlet and boot it up.
If you still get nothing from the system, remove the motherboard from the case and follow this troubleshooting guide:
Out of case troubleshooter. Make sure the cards are all inserted fully into their slots and all power connectors are tight.
Try the system with the RAM or video card removed. When you boot it up, it should beep like crazy telling you something is missing (make sure the case speaker is connected if the motherboard doesn't have a piezo speaker on it already). If it does beep, the CPU and motherboard are probably fine. If it doesn't beep, one or the other might be bad.
The P3 450MHz runs on the 100MHz FSB setting with the clock/multiplier ratio set to 4.5.
Cricket