When you push the "test" button, you should hear a distinct click as the GFCI trips. If you do not hear this distinct clicking noise, then most likely there is no voltage at this GFCI receptacle (or this receptacle could be defective).
When you push the "reset" button, if you hear a distinct click, this means that either:
1) another receptacle "down-line" that is protected by this GFCI receptacle has a defective appliance plugged in, or
2) another receptacle "down-line" that is protected by this GFCI receptacle is defective, or
3) there is faulty wiring somewhere "down-line" from this receptacle, or
4) there is too much moisture in this GFCI receptacle causing it to trip.
You have stated that the two bath outlets are GFCI protected, but obviously you are unsure as to where this protection is. Most likely the protected outlets are protected from a GFCI outlet in the same bath, but could be protected from a GFCI outlet from another bath. This is where I would look first. It is also possible to have a GFCI breaker in the main panel that protects the entire bath circuit. If so, there will be a button on the breaker to push and reset in addition to the off-on switch.
Once you figure out all this and have everything back on, you may want to make a map of your house showing where all the receptacles are, then turn off one breaker at a time and make note of which ones have no power. After that, do the same with your GFCI receptacles, pushing the test button of one receptacle at a time and making a note if any other receptacles that have no power.
I hope this helps. Good luck.