Most likely they were part of the bad capacitor plague. More info at this link:
http://www.badcaps.net/pages.php?vid=9from this website that services and provides service kits for boards
http://www.badcaps.net/It would probably be cheaper to find a good replacement board or similar processing power computer working as a whole than it would be to service this board. The power supply for this system you have may also have bad caps in it and caused an over voltage condition to the motherboard. I would inspect the power supply for swollen or leaking caps as well. If you will be opening the power supply first unplug the power cord from the back of the power supply. Then press the power button on the front of the computer and this will drain the power supply. Then wait about 60 seconds and go in and inspect the power supply and avoid bare skin contact with any circuitry just in case a capacitor didnt drain as for you could get shocked if a cap didnt drain. Most power supplies the power supplies can be opened and then inspected without getting your fingers in harms way. Be very careful if you open the supply and never open a power supply that is plugged into the wall !!!!
The new socket 775 motherboards are starting to disappear due to being obsolete, but some are still available in the RAM types of DDR, DDR2, and newer DDR3. Here is one that takes DDR2 which might work with your RAM if your RAM didnt get cooked when you had this failure.
http://www.newegg.com/Product/Product.aspx?Item=N82E16813157337&cm_re=socket_775_motherboard-_-13-157-337-_-Product I wouldnt spend this kind of money for a new board for such an old system unless you have a really tight budget. And with a tight budget I'd suggest a Refurb system which comes with a warranty. For around $76 they have a Pentium 4 with Windows 7 and this Core 2 Duo for $110
http://www.newegg.com/Product/Product.aspx?Item=N82E16883281287 If buying a motherboard off of ebay etc, you can usually score a good used socket 775 motherboard for around $20-$40 depending on the board. The socket 775 boards that have Core 2 Quad support bring bigger price tags. Be sure to make sure the board will support your specific CPU before buying one as for some socket 775 motherboards max out on a Pentium 4 or Pentium D and cant support a Core 2 Duo. These boards generally sell cheap that dont support the Core 2 Duo or Core 2 Quads. Depending on the processing power needed you could get a working Pentium 4 or D motherboard with CPU and possibly RAM as well pretty cheap if your planning on running XP, Vista or Linux and no complex games but instead games of the era in which the board was made as a good match of processing power to software/games
