yea with your 4830 that sounds like a fairly classic sign of maybe the power wasn't sufficient.
But yes pretty much that is what I am saying. Try the card, even if it fails, it shouldn't damage the card by getting insufficient power. Think of it this way, too much power can fry cards, but too little it just won't work. Worst which could happen is you are without a card or without computer until a better power supply comes in.
The bigger things you need to make sure is that you have the right PCI-E power connections for the graphics card. If you do, you might be alright. AMD graphics cards are based on RISC technology, like in your smart phone but different. So while they can use a lot of power, they are fairly low power usage for the...