Of the 16 blown up eMachines mentioned in this thread, 13 older eMachines have the awful overvolting Bestec 250W power supply, which is a known motherboard destroyer whether it fails totally or not. This can be confirmed at the following site:
http://parts.emachines.com/emachines/
For the newer three that have the less destructive 300W type, T5026, T5088 and T3104, the motherboard is not necessarily fried, if I followed the descriptions correctly. But the PSU is.
On older machines it is clearly prudent to upgrade the 250W power supply anyway. This 350W Fortron is a good short-cabled replacement:
http://www.newegg.com/Product/Product.aspx?Item=N82E16817104901
Doubtless older motherboards also fail regularly, due largely to the industry wide bad capacitor problem and lightning and surges, and I have noticed the newer OEM MS-7207 failing regularly too, perhaps due to the inappropriate 20 pin power supply fitted or overheating of the NForce northbridge. Processor failure is rare in my experience at an eMachines Forum.
Whatever the exact reason for individual failure, a new power supply and suitable motherboard will usually fix it. Socket A is almost unobtainable, but Asrock continue to make suitable mATX Socket 478 replacements such as the P4i65G.
To dispel some of the myths about restore disks and Windows activation, the restore disks/partition will work where the same basic chipset is used for the replacement. Minor variations in LAN and audio are not important, and F8 safemode may get past any issues that do arise. Where you change the motherboard chipset due to failure of the original, you will have no difficulty internet activating an install from an OEM retail Windows XP Home disk, using your eMachines COA number.
Interesting observations by raybay on motherboard failure. I shall mull that one over. Touchwood, eMachines made in the last two years, by Gateway, are much more reliable, and run cooler due to casefans being fitted. Sorry for such a long post.