This sounds like a card failure.
1.Try iGPU/or if possible try another video card to see if your PC is fine.
2.Do you try to clean install Win7? If you have problem to do that on your daily system, do that on another hard driver.(remember to unplug the power cable from the daily hard driver. while you are doing so, keep only one hard disk on system)
Or use ubuntu bootable usb, it is the fastest way to try a PC with an OS but need not have another hard disk & no need to wait for the long install and windows update progress.
Make an ubuntu bootable usb(or any Linux you familiar), with unetbootin tool from ubuntu ISO file. As for the version , use the latest , for now it is 16.04 64bit. Then use it to boot your PC, no need to install it, just boot into ubuntu demo mode to see if your card is still alive or not.
But noticed that the ubuntu will modify BIOS time to UTC(or something like that, I can't remeber), remember to re-configure BISO date time again when you done test.
If the card is still alive, you should be able boot into ubuntu desktop and do something without any video crash issue. In this case, maybe a clean install windows will help you.(still no guarantee)
If not, then RMA the card.
In fact I have similar experience with you. My HD7850 died too. I still can boot into BIOS screen and OS command line with the card, but no way to boot into OS desktop, screen signal will lost soon.