That happened to a Machine i purchased awhile back.
Turns out the soldering inside the PSU was touching the inside of the PSU Casing and causing a short when ever it was moved or bumped.
Wierd but true.....i troubleshooted it for days before thinking of even opening that up.
I had the case lined with Foam, Tried upteen Vid Cards, New Ram, New this and new that, Bench tested it to its hearts content and it never showed problems until i remounted in the same case, but it was one of those (im going to beat you cases) so i never gave up.
lmao....wierd part about it is after we got to know eachother inside and out (comp and I) i sold it............roflmao