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.
Home was where I park it. but alas the.
2005 Damon Intruder 377 Alas declared a total loss
after a semi "nicked" it. Still have the radios
Kenwood TS-2000, ICOM ID-5100, ID-51A+2, ID-880 REF030C most times