Im gonna guess that your power supply isnt very good since you state its a 500 w one that meets minimal requirements. Thats a good way to blow out your PC. Generally low end PSUs have a tendency when they go, to take everything with it. Get a quality PSU, Seasonic, XFX, Corsair before you buy any GPU. Not a piece of crap.
Going cheap on a PSU is not the way to go. Said it before. Can get a good quaility one for a bit more than the cheap ones, spend the cash and then you dont have to worry about your PSU dying and taking out all your hardware.
I personally don't believe it is that hard replacing the PSU because I have done it quit a few times. With that 550w modular one it should be pretty easy. Your HDD have one SATA power connector along with the Optical drives. Your motherboard has one main connector (20/24 pin connector) and another one for your CPU cooler fan (4/8 pin connector). Depending on your case you may also have some fans connected to the PSU by molex/peripheral connectors. Lastly the GPU will have one or two (one for 7850 two for 7870) PCI-E connectors.