Suggest you download a tool like 'hwmonitor' from CPUID (free) and see how hot your card is getting. +1 for installing the latest drivers.
Nice i5 3330 based system, but the PSU is only 300W. At stock clock the 260x draws 115 watts the the i5 draws 77w max so you should be ok. Suggest if the temps are OK and the driver doesn't help that you download MSI precision and underclock your 260x. See if it stabilizes.
Finally, does the black screen happen all the time, or only when playing a certain game? Try alt-control-del and see if that makes the screen reappear with the menu where you can launch task manager.