1st thing id reccomend is to check if there any warrenty left on the gpu. If there is warranty left, i would rma it and get a new one.
If there isnt, you could search for a gpu teardown of your gpu online, follow each step carefully to take the cooler off, and inspect the board for physical damage such as burnt looking or smelling components, or an abnormal white color on the board. Youll need new thermal compound to reinstall the cooler, reverse of teardown. If you find damage, dont try to power the gpu on.
This very well could be the power supply, at the 470 is a relatively power hungry card and could easily stress a psu over time untill the psu fails. This usually has a popping sound, almost like a balloon popped near you, accompanied by blue or white smoke and a sometimes a burnt smell.
Id take both the psu and gpu out, and see if either one smells burnt. You could shine a flashlight in the fan of the psu to see if there is any burnt components or exploded capacitors. The psu is toast if it fails.