Please let me know what BIOS version you have and if have tried flashing the BIOS to the latest version. If not, this would be an option.
I would just suggest not going directly to the latest BIOS version, but rather go 1 by 1 and to use the F7 method.
You can check the following link for the BIOS Update Instructions if needed.
There are a myriad of components that could have failed (or been corrupted) and result in these symptoms being seen (and yes, a failing PSU is a possibility). I would isolate the testing as much as possible - that is, remove the board and PSU from the chassis and place them on a non-conductive surface and connect only the essential components while you test. If you cannot isolate the problem to a specific component (PSU, memory DIMM, etc.) and you are looking specifically at the motherboard, there is little that you can do in the field beyond clearing CMOS and trying to update the BIOS. If the cause is, for example, failure/corruption of the BIOS flash chip on the board, this is not something that can be fixed in the field (only Intel personnel have the tools that can fix this). If your board is still under warranty (i.e. you purchased it less than three years ago), you should contact Intel Customer Support regarding warranty repair/replacement...