Emachines C2825 problem
If you know the motherboard is bad as well, you have two options.
You can salvage the existing case and parts, and replace the motherboard and PSU. Plan on spending around $100-150 for both together. This assumes the CPU and RAM are undamaged.
The second option is to buy a different "bare-bones" system, and transplant the parts into that one (CD/DVD drive and Hard Drive).
Unless you have an exact replacement for the motherboard, you'll probably need to reinstall Windows. The easiest way around this is to install Windows onto a new hard drive, and attach your old hard drive as a "slave" or "secondary".
These two options are centered around off-the-shelf parts, rather than buying a "brand X" computer. If you prefer "brand X", which includes an 800 # you can call, look at Dell. eMachines and Dell both produce low-cost low-quality systems, but Dell is better at it.
For ideas on parts, look at an online retailer like NewEgg. For compatability, this is mostly a matter of using a tape measure and/or counting pins; they have low prices because they aren't there to hold your hand; if you would feel more comfortable with some hand-holding, which is fine, buy a new "brand X" computer.
Lastly, keep in mind, the difference between a $500 computer and a $1500 computer is more than profit margin. If they don't say exactly what a part is, it's whatever was cheapest at the time. A $500 computer may be all you need, but it will have problems like this; whether that's best for you, is for you to decide.