First of all - welcome to BC!
What version of XP do you have? Retail or OEM? If you have a retail version you will have no problem re-installing XP on a new motherboard, if you have an OEM version and you fit a new motherboard, MS may consider it a new computer and refuse to authenticate your copy. If they agree that it is a 'repair', they will normally allow you to do this but you would be best to determine whether or not it is your mobo at fault, and speak to MS before you put a new one in.
I tracked down the topic you referred to by Fred93 and it unhappily tails off without any definite resolution reported. In my experience, problems like this are generally caused by either hard drive problems or video problems.
Have you checked your hard drive for any potential problems? The Seagate HD tools for DOS test disc is as good a tester as any, unless you know that you have a drive from a different maker. In which case download and burn their equivalent test disc. Back up your data first if at all possible.
In Fred93's topic there were suggestions that there might also be a problem with his on-board video, that it worked with generic Windows drivers but not with the manufacturer's drivers. Rather than dumping the mobo, a solution to this problem - if your problem is caused by the on-board graphics - might be to see if you can get a video card to fit into your computer and use the video / graphics via that. Given the apparent age of your computer this might be a problem, but you could always have a look on e-bay.
Another factor for you to think about is, given the age of this machine, is it worth spending time and money on? They appear to have been built about 2003 / 2004 which is a good age for a computer. Even if money is tight, you can get an ex-lease machine relatively cheaply and it would be newer than your present one.