My nephew's computer monitor now only shows "No Video Input" when the computer is turned on (also, not much seems to happen physically when turned on...from listening to the sounds). Anyway, I'm not sure if a video card problem could cause the exact same symptoms, but it doesn't matter as there is not video card! So, motherboard issue I'd have to say.

In the Compaq spec for this computer it says:

Manufacturer: Asus *
Motherboard Name: A8N-LA *
HP/Compaq motherboard name: Nagami2-GL8E

My only confusion is why does Compaq have this motherboard renamed as "Nagami2-GL8E?" I was thinking about watching ebay for a cheap A8N-LA motherboard replacement, but was wondering if the computer must run a proprietary Compaq version: Nagami2-GL8E? Or are the two motherboards exactly identical, and I should not expect any problems?