tHE j0KER: That would only be possible if they could get their machine to successfully boot. As they said, their system is constantly power-cycling, which would prevent Windows from booting, let alone reinstalling a fresh copy. The only way it might help is if it's powering down/rebooting as a result of a startup BSOD.
That being said...
D75Erica: Is it even getting to the Windows loading screen? Or does it not get that far? If it IS getting to that, it's very possible it IS something wrong with the Windows installation. If it's NOT, then a hardware issue is likely, yes.
In addition to eBay, if you need a motherboard, I recommend this site:
I have used them in the past for boards for both my DV9700 and my C500. They're prompt, the boards have always worked and been as advertised, and they have numerous DV4 boards. You would simply need to confirm which board number you have (usually on a label near the RAM slots) and find that replacement. The prices I found with a quick glance were $115 and up.
Replacing the dead board with an identical one is most recommended to ensure compatibility. Alternatively, you CAN replace it with another board for that model, as long as you match the CPU type (AMD for AMD, Intel for Intel). However, you may wind up with different capabilities if you do that (different RAM max, different NB chip, different video, etc).
Just my two cents. Hope it helps you out some!
O Shadow Fox O