|What make and model is the brand name system, or if you have a generic system, what is the make and model of the mboard ?|
What (max output) wattage capacity does you power supply have ?
What is the make and model of the power supply ?
For both the ATI Radeon™ HD 5750 and HD 5770 - System Requirements
* 450 Watt or greater power supply with one 75W 6-pin PCI Express® power connectors recommended (600 Watt and two 6-pin connectors for ATI CrossFireX™ technology in dual mode)
* Certified power supplies are recommended. Refer to http://ati.amd.com/certifiedPSU for a list of Certified products
El-cheapo or older power supplies are less likely to put out enough of the necessary +12v power the video chipsets need.
You MAY be able to get away with using, say, a 550 watt power supply, but not likely less.
If you need to replace the power supply, you can usually replace it with any decent quality standard sized standard ATX PS
Standard (PS/2) power supply size - 86mm high, 150mm wide, 140mm deep, or 3 3/8" h x 5 7/8" w x 5 1/2" d , or very close to that, though the depth can be more or less for some PSs.
El - cheapo power supplies are a lot more likely to cause you problems.
Don't buy an el-cheapo (in quality) PS.
See response 3 in this:
Note - I may have mentioned Coolermaster in that - I have recently found some models have only a 1 year warranty, some are known to have premature fan failures, some are known to develop failing electrolytic capacitors.
Regarding the original card not working....
Did you remember to connect the 6 pin PCI-E power connector to the socket on the card ?
Did you unplug the computer, or otherwise switch off the AC power to the computer, at ALL times, BEFORE you were fiddling around inside the case plugging in or unplugging cards or connections ?.
If you didn't, the mboard is always powered in some places including some of the contacts in the card slots, even when the computer is not running, as long as the PS is receiving live AC power and the PS is switched on if it has a switch. You may have damaged the video card(s) or the circuits of the slot you plugged them in to, or you may have fried the power supply !
If you have fried the power supply, it will not allow any working computer you connect it to, to boot normally.
Try connecting a power supply from another working computer, yours or a friends, if you can, that has at least 450 watts capacity for one card, or at least 600 watts capacity for both of them .
Better quality power supplies have auto features that are tripped and disable the PS from starting up when it has been overloaded beyond a certain point, etc.. The power supply will work normally after a short time, say, 10 minutes, after whatever problem that caused that protection to trip off has been eliminated.
You may need to have the AC power to the power supply off for that long.
E.g. Enermax PSs do that.