You should try following steps:
1) If you have on-board graphics take out the graphic card run windows and uninstall any previous video drivers and then do a fresh install of all the video drivers for the graphic card.
2)Then install you GPU and check if it solved the problem.
Note:In your bios settings the default video output should be selected as : PCIE for your system to use the PCIE graphics instead of on-board graphics. DO NOT disable on-board graphics while doing this(i.e On-Board Graphics: OFF).
3)If still no success then check whether there are any instructions in the manual indicating which display port you should connect to out of the two and do so.
4)If your monitor supports a dvi cable, connect it to any of the two ports on the graphic card, which ever is supported.(one of them is DVI-I and other is DVI-D).You should check with both the connectors on the graphic card.
[Note:
-If you are using a vga to dvi-d adapter I think you should connect to the DVI-D port on the graphic card.
-If your monitor has a dvi-d connector you cant connect it to the DVI-I port first.]
I don't think your graphic card is broken, if your system boots successfully. Its either a driver issue or some installation or connection issue, I guess.
PS: if you have any confusion regarding ports, you can google vga,dvi-d,dvi-i. IReading you previous posts in this thread I am confused whether your monitor has a dvi port/cable or a vga port/cable.