You can try to do a system restore from before BF4 when the issue started happenning.
Try removing any non essential devices from the system (Webcam, printers, etc)
Try restoring CMOS to default values.
Disconnect and re-connect all wiring, re-seating cards, SIMM/DIMMs.
But I think it's time you back up your data, start swapping out parts and get ready to re-install windows a few times.
My recommendation would be as follows:
Motherboard (Most points of failure by far)
PSU
VGA
I would be surprised if the issue is not with one of those three.