What are you system specs? As much detail as you can for your spec would be helpful specially with the Power Supply.
I think its possible to be a fault on the motherboard... need to check on a few details though.
When the PC was on the black screen were the fans running? Ie is power still being supplied to your machine?
When you turn your PC on now does it attempt to start or does nothing happen at all?
Have you tried putting the HD4870 card back into your computer? If not try that and let us know what happens with regard to the above questions.
The more detail you can give on the problem the better for us diagnosing
