I think it is unlikely that you could harm any circuitry by shorting the Vbat terminals together.
You could have drained your battery, if it was in for any length of time, since the + terminal could have shorted the battery + and - together.
So first thing is to try a new battery, inserted correctly.
And do you have your GPS set for Vbat power or Vdd?? If it is set for Vbat, and Vbat is drained, it won't keep time when off.? When you use the GPS for the clock, based on earlier messages in this forum, I understand you need to set RTC control to 'software' (due to a bug or 'feature' of the current firmware), in order for the GPS to continually update the clock.? [And note that the GPS may take a long time to get clock sync when you first turn it on in a new location - at least many minutes.? Subsequent sync times will be much faster.]
Stan KC7XE