hi mate
this is a common issue when installing a new gfx card especially when upgrading from a onboard(intergrated) video device
have you tried accessing your bios setup ,then go to "advanced chipset features" and checking that "init display first" is set to pci-express,and also go to "intergrated peripherlas" and disable your onboard video
note: when doing the above changes you need to have your monitors v.g.a cable connected to your previous vga port,so if that was a onboard video device then connect it to that,then after you have changed "init display first" and disabled your onboard video,plus remember to "save and exit setup" to save the changes to the cmos,you can then swap the vga cable over to your new gfx card,also if theres a dvi port on your new gfx card then use this over the standard d-sub(vga) port,digital is allways better than anologue
other reasons for problem
1) if the new gfx card requires additional power then make sure you have connected a appropriate power connector,try not to use a splitter,you may use a splitter with hard drives,optical drives and other hardware but try to avoid using a splitter with gfx cards,my advice is allways use a connector that runs directly from the psu,most modern psu,s have 6 x 5v molex connectors,2 x sata connectors and 2 x 6pin pci-express connectors,so even with a sli configuration you should have more than enough power connectors
2)check all leads and cables,make sure you have connected the cpu fan power connector to the appropriate socket on the motherboard,and make sure any clips ect on the heatsink and fan assemebly have been secured correctly
3)check all expansion cards (pci-express,pci-express x1,pci-bus) have been correctly inserted,its extremely easy to incorrectly fit any card,especially pci-express cards
4)memory: check all the modules are correctly fitted,best option is to remove all of them and re-insert them,and when re-inserting them fit them from largest(in dimm 1) then the next biggest in dimm2 and so on,however matched pairs and dual channel should be installed as per manufactuers instructions
5)front power connectors : these are tricky to connect however the main one is the front power button,you should find a diagram of how to connect these in your motherboard manual however if not check out this picture :
http://www.hardwarezone.com/reviews/category/others/low_cost_pc/part06/case_connectors.jpg
i have included quite a bit of information on what could be wrong with your p.c however its a case of "trial and error",sometimes the p.c may suddenly start for no reason,i have used computers for over 2 decades and i still dont 100% understand the way they work,and it dosent help when new technology is released every six months
good luck mate !