If you have any bulged capacitors, the board is probably toast.
The memory tester is memtest86, and the last version boots off of CD. There have been further variants of the memtest utility, but the original appears to have ended development in 2004.
http://www.memtest86.com/The "up to date" project (memtest+) hasn't been updated since Oct 2005.
http://www.memtest.org/Either should work for you, but the memtest.org one might show a little more info.
I still think you're gonna need a new mobo if you have blown capacitors. I had a mobo with defective caps and it slowly got more and more unstable to the point where one day it would boot only 1 in about 8 attempts. I almost lost everything on the hard drive that time because it was a RAID 0 array, so I had to buy a replacement mobo with the same RAID controller so I wouldn't lose everything.