You should have a black (maybe red, blue, or any other color but white, gray green, or bare) connected to a brass screw and white (very infrequently gray but also permitted) connected to the silver screw. Sometimes devices are used to feed another device which sounds like the case if you have the aforementioned color combination connected to the other pair of screws. In that case, your best bet would be to connect the existing wires plus the ones for you new outlet under a wire nut and add what's called a "pigtail" (a short, 6" piece of wire) to feed this existing receptacle. You'd do that for both the hot, neutral, and the ground wires. If the box is metal, the ground needs to connect to that as well.

"Actually, it IS possible for large appliances to generate power line spikes. I'm not talking about surges here; those are typically only a couple of percent and are of little significance. I'm talking about short duration spikes, which can easily run into the thousands of volts." That is popular when facts come from speculation and are not based in spec numbers. If an appliance generates spikes as claimed, then a first appliance destroyed is the spike generating appliance. Second, if an appliance is generating such spikes, then you are replacing a dishwasher, dimmer switches, furnace, clock radios, microwave oven, GFCIs, door bell, LED & CFL bulbs, toaster, and smoke detectors daily. How many did you replace today? None? Why? Because those spike do not exist. Third, if a spike is created by an appliance, then we do not put a protector on its victim. Instead we put it on the spike generator. And finally, plug-in protectors would degrade to nothing quickly (days or weeks) if an appliance was routinely generating those spikes. Anyone can read charts from MOV datasheets. Most don't. Most simply recite the first fear promoted by some irresponsible third party with an agenda. Did we not learn anything from Saddam's WMDs? If cutting off power creates that inductive spike, then it is create 120 times every second. 60 Hz power cuts off (goes to zero) twice with each cycle. A scanner was damaged because only observation only generated a conclusion. You did not even identify an internal part that was damaged. Conclusions from observation are classic called junk science. Meanwhile they also made that same conclusion about a computer that had worked continuously for months. They turned it off once. And it would no longer restart. Then one, who first learns facts before making a conclusion, did an analysis. A bootstrap resistor had failed maybe months earlier. Its only function is to provide power on startup. Damage only speculated from power cycling was actually a failure weeks earlier due to too many hours of operation. Again, one learns hard facts long before making a conclusion. The myth of major appliance power cycling is popular when junk science replaces reality. Meanwhile, had one properly earthed a 'whole house' protector, then even appliance generated surges do not exist. That (and not any plug-in magic boxes) is always recommended when a recommendation comes from others who first learn basic electrical concepts. Why do so many install grossly oversized power supplies? Lack of basic electrical concepts is routine among computer assemblers. The informed never waste money on magic plug-in boxes (TVSS, protector, arrestor, SPD, VPR, suppresser) recommended by ignoring spec numbers. Computers rarely consume 350 watts. And consume somewhere between 100 and 200 watts most of the time. Household appliances do not create those massive spikes. Potentially destructive spikes occur maybe once every seven years. And are only averted by a properly earthed 'whole house' solution. How often do you suffer such spikes? A number that can vary even in the same town. So an informed homeowner learns neighborhood history from a past 10 or 20 years.

I agree that a tripped GFI somewhere ahead of what you have is the most likely culprit. The challenge is to find it. Look behind furniture. Check in the cellar, especially right under or nearly under the bathroom. Look in the garage, including behind stuff. It might even be outside. When GFIs were new, they were expensive. Fairly often, a single one was daisy-chained to some or all of the other receptacles that the code said had to be protected. It's not common for a second GFI to be fed from a first, but I don't know of any harm that can cause. As for why it would be, it's possible that a previous owner didn't know the bathroom receptacle had GFI protection upstream (if it does), and added another. Another possibility is a loose connection on a receptacle that feeds the first dead one. That receptacle itself would still work if one of the downstream terminal screws were loose. Parenthetical anecdote: one of my rentals is a late 1950s tract house. I lived in it myself for a while, and during that time I did a little electrical work on it. I was astonished to find that on NONE of the original receptacles was the second set of terminal screws used. The electricans who wired the house -- and remember, this was not an expensive custom home -- actually made up soldered and taped connections in each box where there were receptacles downstream. The soldering was clean, too. No cold joints that I saw.

Can't really tell where on your diagram your photos are, but, first, understand that you're going to have to break into the drywall in several places and later repair that. Get into your breaker box by taking the front off. Do that and post a picture of it. If you're lucky, there will be breakouts in the top of the box. Find a place above the box in front of an available breakout and a point at the wall-ceiling corner directly above that place and break a hole in the wall and ceiling there. I assume you're going to use Romex or equivalent. Run your wire toward the unfinished room. Once there, you're home free. Once you get around the stairs, can you go behind them and run the wire over to where the fireplace will be? I would make all the access holes before you start.