Odds are pretty good that you have other outlets wired to the GFCI outlet... I'd look at other outlets possibly outside and see if any of them are dead too and may be damaged. I've run into this on newer homes here in Tucson. The single GFCI outlet will have several outside outlets attached to...
Another option would be to set it outside behind the shop. I have a small compressor 20-30 gal tank and to get more storage I went and bought two 30 gal propane tanks... decompressed them, removed the valves, filled with water and then pulled a vacuum on them to remove any excess water. I set...