According to the AMD official system requirements you should have at least 500W PSU for that card. However, 480W is pretty close. So as long as you don't have a ridiculous amount of peripherals (tons of case fans, HDDs, Optical drives, etc) and you aren't extremely OCing your parts (RAM or CPU), you should be OK with your 480W PSU.
Over time a PSU can diminish, so if it is very old you may want to consider getting a new one. Here's a relatively decent PSU calculator site for your reference: http://www.extreme.outervision.com/psuca...
You may need to upgrade your power supply to a 600 watt as the card is very powerfull. You would regret only getting a 1gb VRAM version, get 2gb. :).
Most likely it is your power supply. Look on the side of the power supply it should give you a chart of what your power supply puts out. What is that?
Does the PSU put out 38 amps on your +12 volt rail? If more then one +12 volt, does two of them add to 38 amps and are both plugged in to the card.(since there are two plugs for pci-e) Are the pci-e plugs connected to each other? If they are, then its the same +12 volt rail.
Find two that aren't connected.
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