Outside of my house there are two outlets(one GFI and one 3 prong) next to each other. Neither outlets are working. I hit the test on the GFI, which popped out the reset button. I can't push the reset button back in. There are a couple other indoor outlets that run off the same fuse which work fine.

GFI's can go bad very easily. I had one in my bathroom that went bad after only used for one year. Just replace both.

Outside GFI's are very susceptible to moisture, lightning etc. The other 3 prong is probably run off the load side of the GFI. Replace the GFI and wire the other 3 prong through the load side, that way it is also protected. Harbor Freight typically carries them for $8