|Generally speaking the motherboard is the key component that Windows uses to determine hardware originality. Changing the motherboard may well cause your OEM version of Windows to no longer work.|
That said, you would need to use a replacement board that has the same CPU socket type and sues the same meory type too.
According to the HP site your board has an AM2 socket, which is not that old.
Have you checked to verify it isn't covered under warranty?
The link below shows your specs and there is a link for warranty there. I suggest you first pursue that option.
As jam stated, bad capacitors was a problem dating back more than 5 years. I guess it is possible but I would like to see a photo of the bulging capacitors. Do you have the motherboard or the whole computer in your possession? If so, take some photos and upload them to a site like photobucket and post the link here in this thread.
Googling for "bad capacitors" will yield many hits. Below are a few.