Probably Not the Answer You Were Hoping For.......
The problem with replacing the motherboard in an Emachine is the extravagant price they will charge you. Also, the power supply is most probably also bad, either by virtue of it killing the board, or being killed by it. I absolutely do not recommend buying a board off Ebay, that's sort of asking to be ripped off.
Here's the specs on your machine
http://www.emachines.com/support/product_support.html?cat=Desktops&subcat=W Series&model=W3503
That's pretty much bad news as well, since the Emachine in question has DDR type memory, which would likely have to be replaced with any board you might find today.
The standard treatment for this is to buy a different aftermarket board, and a decent PSU. However, the copy of Windows that came with the machine dies with the board, and would have to be purchased also.
This is representative of a type of board that would fit your chassis;
http://www.newegg.com/Product/Produ...rder=BESTMATCH&Description=Intel+G31+&x=0&y=0 and allow you to use your CPU. These boards are about 50 bucks. A replacement Emachine board might be on the order of up to 200 dollars. The upgrade parts I mentioned can be had for about 300 dollars, including the copy of Windows.
http://www.newegg.com/Product/Product.aspx?Item=N82E16832116752 This is the OEM version, and you would need to order it with the parts.
As I said, you would also require new memory, a PSU, and a copy of Windows.
PS, The Celeron 356 in that machine is a "Cedar Mill" chip. These were the best single core Celerons (Pentium 4 type architecture) produced. (Until chips based in the new "Core 2 Duo" technology became available). They are however, less than pitiful by contemporary standards. Again, sorry if I ruined your day.