Graphic card fan stopped working and pc boot problems

I am having problems with my PC, when I booting up my PC everything seemed working fine except the screen wouldn't respond. I had quick solutions to this by replacing the cmos battery with another, but this wasn't always working and I couldn't find a Permanent solution for this problem. Today I tried to change the the cmos battery again because my screen was not booting, and I touched accidentally with the battery the graphic card and it made a little spark. Since then the graphic card fan hasn't working and I couldn't make the screen boot with the PC (although the screen wasn't working before the spark) and I am not sure if there is a solution to this , or maybe the fan died and I need to replace it or the graphic card died? How can I check where is the damage ? And what can I do to fix the screen not booting problem?

Thanks a lot for reading and trying to help!