Overheating would be my first thought as well. There are a few other possibilities I'd look into, though, if I were you:
1. It could be a faulty memory module. Download and run memtest86 to check that all the modules are in good working order. I'd also suggest taking them out and putting them back, just to make sure they're seated properly.
2. The video card might no be receiving enough power. If the specs I'm looking at are right, the video card you've got in there was an add-on, correct? It's possible the pre-existing power supply doesn't have enough juice to power the newer card when the system is running at full load. I wasn't able to find a spec on what PSU eMachines might have put in there, so I can't say for sure.
3. It could be a timing problem. If you've done any overclocking, the CPU might be talking faster than the memory can listen. When this happens, the result is usually a memory dump, followed by an instant shutdown. This is a very common problem with overclocked systems. SL stresses the system more than most other programs, so it's not unusual for this type of problem to rear its head while SL is running.
4. It might be a voltage problem. Go into the motherboard settings, and make sure the voltages are right for every component you've got plugged in. If you upgraded the memory, it's entirely possible that the newer modules have different requirements than the older ones.
4. Something might be badly seated. Remove all components, and put them back in place. Sometimes a simple reseating can solve any number of problems, including the kind you've described.
If it is overheating that's the issue, here are a few things you can do:
1. Make sure all wiring inside the machine is neatly bundled and tucked out of the way. A sloppy case is a hot case. Unimpeded air flow is absolutely imperative.
2. Make sure all fans are clean, and in proper working order.
3. Add more fans, if you can, and make sure they're blowing the right directions. Typically, front and bottom fans are intakes, and rear and top fans are exhaust.
4. Invest in a good CPU cooling system. I'm a huge fan (no pun intended) of the Zalman 9500 series. The chip you have is socket AM2, right? This one should fit:
http://www.newegg.com/Product/Product.aspx?Item=N82E16835118223 I've got the exact same one in the machine I'm using to write this post, since it also fits Intel socket 775, and I absolutely love it. My CPU temp went down a full 10 degrees when I switched to it from the liquid system I'd had in place before.
5. It could be the GPU, not the CPU that's overheating, so make sure you've got a good cooling system on that too, and that it's got unobstructed air flow all around it.
6. Clean out all, and I do mean ALL, dust and debris from isnide the case. A can of compressed air, and a vacuum cleaner go along way. (Note: Don't touch any components with the vaccuum nozel, as that could cause a static discharge, and fry them. Hold the nozel a few inches away, and use it to snatch the dislodged dust out of the air, as the compressed air sends it flying off.
That's about all I can think of off hand. Good luck.