Sounds like a good candidate for the bad caps (google it) issue. Given the relative scarcity of P4 boards these days, you may not have a lot of choice beyond scraping it.
PC Freezes in BIOS and Randomly..And Not Starting?My Dad's 7 Year OLD PC hangs(Freezes) In the BIOS and when in windows. I have tried everything from Re-installing Windows 7 and Installing New Ram.....But nothing works...It freeze and i have to force restart it by switching it off and then back on. This is Really frustrating. And Now its not even starting. Monitor doesn't respond but the processor fan works and the green light in the motherboard does glow. Since its my Dad Fav PC i just don't want to scrap it. So please try to figure what's wrong..!!..Here's Pc's specs-Intel P4 Processor 2.4 Ghz2GB RamIntel 845GVSR motherboardWindows 7 Home premium Seagate 500GB HDD (5-Years OLD)Please Help!! and Thank you!

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic