Did you plug correctly the 6-pin connector for your HD 6750?
Did you insert correctly and fully the graphic card in the PCI-E x16 slot?
Did you disable the integrated graphics in the BIOS?
Did you plug your monitor to the graphic card itself after doing the previous step?
Did you make sure that you have a 450W+ PSU?
Did you make sure that your card isn't dead by trying on a other computer?
Try all those steps above, they are common mistakes that everyone makes.
Hope it helps!