I've had similar issues with the BIOS in the past when I've had power brown-outs.
The symptoms you describe point to a corrupted BIOS. ASUS is pretty tollerant with corruption, which is why it appears to work, but you get weird stuff happening.
The easiest way to fix this is to check which version of the BIOS you have, download that version from ASUS's website and reflash the BIOS.
M.