An HD 7750 would run fine on that power supply (the stock Dell 305w). Its more power efficient than AMD's old cards that didn't require a six pin connector (like the HD 4670, 5670 and 6670) and is about as powerful as the HD 6770 was. It may be overkill for your CPU though. What CPU do you have in that model?
Apparently you did not read his OP carefully, he currently does not have the 6-pin.
@Hairyola: Some (old) Dell systems had proprietary PSU/mobo wiring on the 20-24 pin connector, had some wires swapped around. If you replace your PSU with a standard one, and you have that wiring scheme, you will fry something (your mobo or the PSU)! That said, I think they were before 2006, but I am not sure. As they said, do not bother putting $$ into your old system. Sry.