Outside AC outlet

First: If the GFCI is tripped the outside outlet WILL NOT WORK.. that is called working as designed.

However you said it would not reset.. There are three reasons that can happen.
1: No power to GFCI (Breaker tripped, Broken wire or connection)
In this case it absolutly will not reset.

2: Ground fault remains: In this case it will reset but immed trips.. IF you are not sure listen carefully as you reset it a few times,, then turn off the circuit breaker feeding it and listen again. .Different sound then option 2.

This problem has two causes.. One is water inside the outside outlet box,, OR a junction box on the GFCI chain.. But usually the outside outlet

The other is something plugged in with a ground fault. UNPLUG EVERYTHING.

Third cause is a bad GFCI, they do go bad.

Remove the GFCI receptacle from the wall. Disconnect the wires on the load side. See if GFCI resets. If it does, there is issues in the receptacles fed by the GFCI. Normally corrosion.
If it doesn't you have a bad GFCI receptacle. Go to locate hardware store and pick up a good quality replacement.

Most of the newer GFCI receptacles have a built-in safety feature that will not allow them to be reset if the GFI protection within the receptacle has failed. When in doubt...change the GFCI out.

GFI outlets do go bad and replacement is the only fix. If you have a meter and feel comfortable around 120 volts, just pull the outlet out and check to see if it has input power.