According to the specs I found on eMachines’ Web site, I’m guessing your T2893 is 7-10 years old. It has a Celeron processor, 512MB of RAM, and an 80GB hard drive. Your actual configuration may vary, or perhaps you’ve upgraded certain components over the years, but trust me when I say this: it’s time for a new (or at least newer) PC.
It’s not that replacing a motherboard is terribly difficult (though it can be if you’re not accustomed to monkeying around inside a PC case). But when you’re done, you’ll be left with the same slow, out-of-date machine you have now.
My advice: look for deals on refurbished desktops. I’ve seen some nicely equipped systems (that include Windows 7) for as low as $279. If you don’t mind used gear, you might find an even better deal on eBay or Craigslist.
There are other considerations, of course, but I’d think twice about putting time and money into a system as old as yours.