Will my macbook pro come back to life with a new graphics card?
Graphics cards on MacBook (and PowerBook / iBook) machines are soldered to the logic boards. You'll likely find a replacement logic board for less than the tools / skills needed to repair things.

If you're into microelectronics repair - you might see about reflowing the GPU and testing - it really depends on the failure profiles for your specific model. Apple normally charges $300 to repair all parts in a Mac portable that fails - so give the manufacturer a chance to repair things. 2010 might be vintage so you'll need to find parts on the open market in all likelihood now that it's 2017.