The motherboard is ok at most things like basic overclocking(nothing to high) and single graphics card solutions. The 970 nb chipset is very limiting with the four plus 1 powerphase and having only one pcie2.0 x16 slot running at full speed and the other running at x4 kinda makes any crossfire attempt slightly weaker than it should be. the reason i know this is that i am running a crossfire config on my system right now.
moral of the story buy the best mobo you can afford so that you can get the best performance out of everything. This motherboard is what is holding me back. if you want to know whats overclocked on this mobo let me know down below.
the card keeps crapping out because it likely reached max temp for to long once and the bond weakens each time you fix it. that is just my thought on it
best advice get a new card and mod in better cooling. the less work you do on the pcs hardware the better off you might be. mod ideas putting in high airflow fans if possible or adding a non stock heatsink(may require computer case mod). in any case these may not all be easy.
i anticipate that when you cleaned everything you removed mobo from its position. if that is the case make sure your not grounding out the mobo at any point. im certain ypu did that already.
remove as many components as you can like graphics cards. networking cards, all drives except you target harddrive and media. it is preferred to use onboard graphics. if the problem persists consider removing the harddrive and use a bootable linux dvd or usb. at this point we have ignored the cmos clock and battery issue in hopes that the problem has fixed itself.
seeing as you have access to the bios try to reflash it to ensure it is the most updated and not corrupted.
good luck buddy i hope i didnt post what you have already done.