Do you have an on board graphics device on your motherboard? You're really SOL without being able to test your card in a different computer, but my suspicion is that something went horribly wrong with your card, although most newer cards and i believe this applies for the 5770 is that they'll protect themselves from getting damaged (heat), you may have had some other sort of issue such as a power surge or possibly your pci-e slot meeting its demise from the heat of the card.
Definitely not my monitor, as i have already tried it using my dad's laptop, works fine . its brand new btw.
Definately not cable as i have tried a dvi cable, instead of the vga w/ a vga - dvi adapter that i use now.
I'd say it'd be your GPU. At first I thought it might be the PSU but you said everythings is poewring on. I would also say it may be your RAM, but you've used your comp before so it probs isnt a bad config or anything. But if you some spare RAM sticks try putting them in and see if you can get the POST to show up.
I'm pretty sure i do not , Actually i could test my card in a different computer, but not for like a couple of days.. I bought the card from a friend that does in fact treat his cards well, although i'm not the original owner.. Usually when this happens after a day or 2 it will work again, i will try to set the fan speed down to 30% because its on default atm, which could be causing it to go boom boom.
Yeah as iverson said when i bought new ram, mix and matching could fuck shit up. Except i took out my new ram, tried it again, and it didn't work.. My PSU is fine cuz everything else powers on, i dont have a problem with buying a new gpu though.