It's a sign of the times, that you'd get proper, solid CAPs if you pay for them and they're usually installed into the "premium" version of things.
http://www.gigabyte.com/microsite/11...hyusesolid.htm
If you're getting BSODs, it is normally a HW problem. If not for a stack overflow on a driver, which could be then hopefully solved by loading newer or older version of the SW / firmware / BIOS.
If component is failing (thermal wear ..) the BSODs typically present themselves in a regular manner. I understand that is not the case. Graphics card, MB, CPU itself or memory modules all could be the culprits. Another possibility is a damaged / improperly connected wire if the inside of the case had been fooled around with.
With the description you provided, me thinks old PSU with yes - leaked capacitors. It could serve well in normal situations, but enter a disturbance in the power grid (harmonics from oldish dryer, neighbour's bench saw) and the PSU with failed caps will deliver power to the box beyond specs the individual components can handle.
Having said that, troubleshooting electric gremlins is a complex task even with the unit physically at hand, all the above is nothing but a speculation.