Paul_cz: It is clear there is something wrong with your hardware. Try to borrow another graphics card or power supply from someone and test it out, or try to underclock your card. But if it does not handle even default clocks with complete stability, it is probably worth replacing anyway.
I would start out by getting a can of compressed air and opening up your computer. Blow out all the dust, and do a careful visual inspection. What you're looking for is any component that looks burned or damaged.
Electrolytic capacitors (little beer-can-shaped things, with what looks like a letter "K", "Y', or maybe "X" on top) are the most likely to fail, especially on a computer that is several years old, especially if you've had heat-related failures before (and the OP definitely has), and especially if it was cheaply made. If it looks like the top has swelled or popped, even a little bit, it's dead.
If your computer has on-board graphics, pull the 4850 out and see if it will POST with the on-board graphics hooked up. Also try with just one stick of RAM and see if it will POST. Try with the disk drives disconnected and see if it will POST.
If you can find no obvious failures, the first component to try replacing is the power supply. Do not, no matter what your lack of funds suggests, get anything less than a top quality power supply. Cheap power supplies
will fail and take other components with them when they do.