New graphics card gives causes reboot shortly after start-up then gives a black screen

Before installing the R7 card are you completely uninstalling the drivers and software for the GT610? When performing this uninstall operation try using driversweeper (or similar program) to completely get rid of any leftover NVidia drivers before installing the new card.

^^^ What he said!

I Helped someone else with this, so I'll just copy-paste my response, THIS IS WHAT HELPED WITH ME, BOTH TIMES
Hey I had this problem too for two days, I found out after doing a complete reset of my computer, and then downloading the drivers that I got from the manufacturer, and when I got to the catalyst driver, and restarted as they recommented, I was back at the black screen again, so now I thought I at least knew what was causing it.
THERE ARE TWO WAYS OF SOLVING THIS
one is If you can get to safe mode
1. while in safe mode, press start, then controlpanel, and then drivermanager or whatever it's called where you can see all the different drivers you have.
2. Find your graphicscard/screencard (whatever it's called) and DELETE IT, don't deactivate it, just DELETE IT, in my case my computer had a graphics card as "backup" but I am not an expert so I'm not sure everyone has that, but I believe everyone does

THE OTHER WAY IS IF YOU ARE ABSOLUTELY LOST AND CANT DO ANYTHING (TOTAL RESET OF COMPUTER)
This is (in my case it was) for windows 7, I don't know if the installer will be the same for windows 8 or others.
Follow this website for visual help with how the installer should look like: www.sevenforums.com/tutorials/1649-clean-install-window...
1. if you still have your windows installer DVD that you got with the manufacturer put it in your computer
2. as your computer is rebooting get into your BIOS menu, don't worry, your computer is designed so that you can get in there even if you dont have a screencard/graphicscard.
3. somewhere you can see "prioritied at boot" or whatever, just make sure that it has the DVD as TOP priority
4. reboot again, at some point a black screen will appear where it says "press any key to.." just do that, hurry you don't have much time, and if you miss it you have to reboot your computer once again.
5. Now the intaller has begun and you can see on the website the steps
6. Go to picture 7 on the website! Do you see how "Driver options" is outlined? press it!
7. Now press format hardrive (on your preffered drive or whichever drive you consider your "largest" drive)
8. WARNING: This will delete all your stuff, so I suggest going into safemode that has internet and then backing up your stuff!
9. Wait for the installation of windows to finish
10. you now have a freshly wiped computer, DO NOT DOWNLOAD CATALYST DRIVER AGAIN (unless it's a different version of driver)

I pretty much wrote this in 5 minutes so if you need my help with explaining anything or rephrasing anything just tell me
(same, just ask, even though it's a copy-paste, if I can help anyone with this it would be great