The rest of the basement is not wired to the GFCI outlet, it is dedicated to the fireplace. The only reason the outlet exists is to provide the GFCI required for the fireplace. Sounds like the OP plugged the compressor into it and that caused the problem.
Good knowledge for all of us, thanks.
John Arenz N6YBH
2017 Cornerstone 45B, 2012 JK Rubicon in tow
2014 Anthem 44B (sold)