The card should be about 70 watts max on it's own. Since your CPU is likely not really putting out 300 watts, I would change it for a better one. You can get a 350 or 400 watt EVGA, XFX, Antec, Seasonic, Rosewill for maybe $40 and won't have a risk of killing the system.
Although going by the fact that you are installing a 10 year old video card it's likely that a new power supply would be as much as just replacing the full computer with a newer and much faster one.