Sounds to me like the PSU is dead... replace it with a known working PSU... if the problem persists, check all motherboard power and digital connections and reset the BIOS with battery off for 5-10 minutes. If the problem still exists, the motherboard is probably dead... the computer is an old model so a dead motherboard wouldn't be surprising.
If a dead motherboard should be the cause, upgrading it with a modern Motherboard, Processor, RAM and a compatible Power Supply would be a great improvement in system performance. You could buy a motherboard with SATA and IDE support so you can reuse your hard drive and save on the total expense.