Since you have the same results with and without UPS, I advise going back basics and stress test the build.
Prime95 for an hour using CPUID's Hardware Monitor (with Detect Rounding Errors checked) to watch temps carefully. Don't let it exceed 75C continuously. If it crashes, you likely have found a memory issue that memtest did not detect.
Then Furmark stress test, not usually crucial with onboard graphics, but do it anyhow.
Then both for say 15 minutes, watching temps very carefully.
Let us know what happens.
Download links available here:http://forums.tweaktown.com/gigabyte/30530-latest-overclocking-programs-system-info-benchmarking-stability-tools.html