I suggest the following well proven technique for fixing hardware problems (when diagnostics such as Memtest86 and Intel Processor diagnostics all pass).

Disassemble everything and as you go:
- Examine the board for loose pieces of wire, solder balls, IC packages with pins bent together, burnt areas, burnt electronics odors, signs of heat.
- Examine for connectors installed backwards or in off-by-one positions.
- Examine CPU pins for folded, missing, oily, or dull contacts. Don't use an eraser to clean CPU contacts. If needed use isopropyl alcohol.
- Examine CPU socket with magnification looking for bent pins. You may be able to fix bent pins with careful use of a needle.
- Examine all other board connectors for foreign matter (like bits of clear plastic packaging, paper, cardboard).
- Examine all cable and board connectors/sockets for pins that may have been bent over or broken off during assembly (e.g. USB connectors)
- Examine memory sticks and contacts for signs of damage, corrosion, oils, or plastic stuck to surfaces.
- Examine the case and the board where mount screws go. check for metal bits, standoffs where there is no mount, screw head misalignment.
- Inspect power supply cables for damage. If the PS is modular, make sure cables are not damaged and that none are loose at the PS.
- Check all jumpers on the MB are installed correctly, the right size, and that no jumpers are missing their metal contacts.
- Verify that both power cables are plugged into the motherboard during disassembly (and subsequent reassembly).
- Inspect the graphics card contacts and any visible parts for damage irregularities. Were power cables populated correctly?
- Inspect all power and data cables for damage. Molex connectors can get spread so they make intermittent contact, for example.
- Reassemble to the minimum configuration needed to power on and run your computer and verify it is working correctly.
- Add remaining components back one at a time and verify correct operation after each one.
- If you have a voltmeter, verify the power supply is providing stable voltages at the right levels.

When everything is inspected and disassembled, inspect again as you reassemble and double check everything against the manual.

In my experience, careful inspection can find the cause for bad hardware about 75% of the time. Even if you don't find anything during this process, it is remarkable the number of computers that will inexplicably work fine after you've disassembled and reassembled them.