If your kids computer is running slow, chances are you could get improved performance by 'cleaning' it up and ensuring it is cleaned of all viruses and malware, however, you could get the same results (actually better) if you were able to just completely reinstalling the OS.
Depending on the machine, you could do some pretty cheap upgrades to make it more viable - check
Ricosuave's thread in Buy and Sell for some RAM upgrades (often the cheapest and easiest to do). If you could post some specs on the machine here, I am sure someone could easily point out the right parts to get and how to install them.