It could be the mobo but if moving it can cause problems I would suspect the power supply or a loose connection. Pull the 2 power connectors to the mobo and see if any of the pins looks dirty or burnt causing a bad connection. While your checking the connections grab a philips head screwdriver and make sure the mobo is secure. Check the cpu heatsink. Is it tight or does it move easily (it should move a little).
Download Hardware Monitor and install and run it. It will show your your temperates and voltages. Leave it running as your using the PC and observe your temperatures and tell use what range your seeing. I also want you to observe your voltages. Are any of them running low? Are any of them fluctuating? Can you post us a screenshot and list your system components by make and manufacturer?