It will cost you more than $20 but your power supply is inadequate. The standard for the 7870 is 500 watts. The Sapphire card also says 500 watts. For some reason the Sapphire card also has two 6 pins istead of the one standard.
Get this XFX 550W http://www.newegg.com/Product/Product.aspx?Item=N82E16817207013
It is a better quality than the CX Corsair and it has the wattage to power your system for it's lifetime. It also has the two pins required.