Seems like the typical OEM 300 watt. It should run fine with a 7750 and would be my choice as a 6770 pulls more power. If you can open up the comp and list out the voltages and the name of the company on the power supply it would be most helpful for further assistance.
It most likely is in the top corner and has a bunch of cables protruding from it connecting to the rest of the components.
Also do you have a budget? That would help out as well.