Your bathroom may have two problems, but let's tackle the GFCI first. When GFCI's first came out there were pretty expensive and the requirements for receptacles that needed to be protected were different than today. You probably want to look around see if you can find any GFCIs that are tripped. It could even be in the garage or basement.

It seems odd that one receptacle in the bathroom worked and the other didn't, because of the GFCI. Typically both would be on the same circuit and therefore both would be protected by the GFCI. My first thought would be there there's a bad connection at original, non-working receptacle. Although it's possible that a previous owner added that receptacle and it's not part of the original bathroom circuit. I would suggest being extremely careful if you decide to pull the receptacle because at this point you have no way of knowing if the wires going to it are live.

A) Houses do not have wiring diagrams.
B) If you have no electrical experience then tracing and troubleshooting will be next to impossible.

I recommend calling an electrician and chalk up the experience to NOT have your bro-in-law do ANY more electrical work in your home.

Alright thanks for the responses. The problem was there before my bro-in-law just turned off the power and installed a light. I probably will call an electrician to tackle this problem.

I'd follow Mike Kaiser's advice. Look in every other bathroom and at any exterior or garage or basement receptacles and see if you find one with a GFCI that may be tripped. It was common back when these things were new and expensive to just daisy chain all the required outlets off one of them. I had a similar hunt to find it in my 1970 tract house. It was in a little used powder room off the laundry room.

I went back and looked and did find a tripped GFCI in our converted garage, thanks Mike. I appreciate all the other responses also.