is this a ver 1 or a ver 2 motherboard? v1 boards are sandy bridge only, although some v1 boards have been able to run a single v2 cpu most have some issues doing so
if you are running a v2 cpu in a rev1 board, try replacing the cpu with a cheap test (sandy bridge) cpu
i've had 2 systems that failed with the same symptoms you describe, due to time restraints we never spent a lot of time on either board, but our rather limited testing indicated a board failure rather than a corrupted bios
not what you want to hear i'm sure
if you do look for a replacement board, don't overlook a bare bones system as sometimes the pricing on them works out better than just a board as you get many spare parts!!
and last, make sure you get a board with the later bootblock date 03/06/2013 which supports the v2 (ivy bridge) cpu's
board revision numbers 1.x to 1.03 are not indicative of a v1/v2 motherboard, however there was a rev 1.04 board that saw limited release late in the z820 life cycle which appears to always be a v2 board