Im not sure what the brand of PSU it is, I bought it at Best buy, this is before I knew anything about computers. I would never go to there now lol. I do know her CPU is AMD Phenom II X4 965 Black Edition Deneb 3.4GHz (125w)
Look at the data plate on the psu to identify it. You should also see the amps available on the +12v rails.
In a simpler way, see if it has a 6 pin pci-e power cable.
If it does, then it should be able to power any discrete card that requires just one such connector, like the 7770.
If it does not have such a lead, then you are restricted to cards that are powered entirely by the pci-e slot.
Like the 7750.
Any stronger graphics card needing two 6 pin connectors will require a psu change to support it.