That really is the best thing to do regarding the PSU, think of a PSU as you would a human heart that needs to be able to pump a good clean blood supply around the body, a PSU is the same as in it needs to be able to produce a clean, stable and adequate power supply to all of your hardware, any interruption or weak supply will result in either an unstable or an unbootable computer.
When you replace the PSU make sure that it meets the following criteria, it needs to be a minimum of Bronze rated, preferably 500W, for the video card you have it must have a minimum of 29 amps on the +12V rail and go for a proven good quality brand such as Antec, Corsair, EVGA or Seasonic.
Finally, if you need help with choosing or would like a second opinion on a PSU that you are considering let us know, and please have the person from who you obtained the card confirm that it was working without issue when they passed it on to you, I`m quite sure that you would not be happy if you replaced the PSU only to find out that the video card was also faulty.