An old PSU with no manufacturer details or brand is not a good one. Realistically, your PSU is actually a 300W one when it comes to a modern PC, not a 500W one, based on the rails and made by a junk OEM manufacturer. That is absolutely not a PSU I'd be running a GPU on with power connector adaptors -- those OEM PSUs are made to be passably OK for the original build and nothing more. Even a fairly low power one like the 650.
I'd either upgrade the power supply to a safe, modern one or put in a 750ti -- the latter still making me uneasy because on an old power supply with old parts, sometimes all it takes is to suddenly need more juice for the PSU to give up the ghost. And in the case of a poor power supply, like the Egyptian pharaohs, take some of your other parts to the tomb with it.