I have just tried to have several games on BF4 and the longest it has last was about 5 mins before black screening.
Performance wise I am quite happy, it is averaging at around 100 FPS with stock CPU in DX11. So a decent jump over the 680 it replaces.
I will try the mantle drivers, a) to hope that some form of mirical happens b) to see the extra performance gains.
Edit: it just Black screened with 14.4 drivers.
I think for some reason 290 cards have a problem with some Gigabyte motherboards. Have you tried the very latest/beta motherboard bios?
It does sound worrying that your box was opened though. I'd be DSR'ing if it was me unless it was a good clocker and or issue free.