Do you heard any Beep! when you turn it on? If no, then the computer don't even finishes it's power on self test (POST). Check that the computer is properly plugged to a power outlet. Check the power supply and it's connection to the motherboard.
That computer may not support USB keyboard and mouse on the BIOS level. Try with a PS2 keyboard and mouse. Those have a small round connector with several connectors surrounded by a metallic cylinder.
It's possible that there is no operating system installed. Once an operating system is installed, the USB ports should be recognised.
It's also possible that the USB ports are defective. If that's the case, it's also probable that the whole motherboard is on the verge of failing.
Kualinar, March 2010