2004 Ford Taurus check brake system light

Was that brake warning light red or yellow?

Everything you described are typical symptoms of a failing generator. The insane engineers have added very unreliable computers to every part of a car that never needed a computer before, and they are very intolerant of low system voltage. They'll do all kinds of weird things, and some will shut down completely.

There's a couple of different ways the generator can fail. Most commonly worn brushes will make it stop working completely but that almost always starts out being very intermittent. Any testing has to be done while the problem is occurring and the "battery" light is on. It can also produce a maximum of exactly one third of its rated current if one of the six diodes fails. 30 amps from a typical 90 amp generator is not enough to run the entire electrical system under all conditions. When the battery has to make up the difference, system voltage will be low and computers can get confused and do strange things. A bad diode rarely fixes itself and starts working again, (unless it has a bad solder connection), so that will show up on a professional load test even if the warning light isn't on at that time.

We don't get involved with costs here because there's way too many variables. We don't even know what's wrong yet.

Unless there's something on your car I'm not aware of, the red brake light turns on for one of three possibilities, and normally none of them are computer-related, therefore, it also isn't influenced by problems with the charging system. The least serious cause is a parking brake that doesn't fully retract. That can be due to a stretched cable that needs to be adjusted a little tighter, but on Ford products it's also real common for them to rust tight inside the casing, then they won't retract and pull the pedal up or the handle down. You can verify that by just moving the pedal or lever manually to the fully-retracted position.

The second cause, and probably the most common one is low brake fluid level in the master cylinder reservoir. That can be due to a leak, but typically it is a result of worn front brake pads that are ready to be replaced. As the old linings wear down, the pistons in the calipers move out about 1/2". That is the self-adjusting feature of all disc brakes. Brake fluid fills in behind those pistons. That's why the level in the reservoir goes down. When new pads are installed, those pistons have to be pushed back into the calipers as far as they will go. That pushes the brake fluid back up to the reservoir. That is also why a conscientious mechanic will never top off the brake fluid during oil changes and other routine service. That would make it over-filled when the new pads are installed, and the excess fluid will spill out and make a mess. Brake fluid also eats painted surfaces.

The third, and most serious cause is unequal pressures in the two brake system hydraulic circuits. That can be due to internal leakage in the master cylinder, especially if the brake pedal was recently pushed all the way to the floor, but more commonly it's due to a leak in one of the systems. With a leak, no pressure can build up in that half of the brake system to apply two brakes. A "pressure-differential" valve shifts position and turns on the warning light. Due to design changes in the suspension geometry for front-wheel-drive cars, if it wouldn't be for that warning light, you might never even know you lost half of your brakes. With only one front brake working, you would expect a very hard pull when stopping, but because of the suspension systems, all you might see is a little wobble in the steering wheel when you first push the brake pedal. Only Chrysler has it so perfected that even the steering wheel stays perfectly steady. GM has a valve that trips to block brake fluid from flowing to the leak. Those need a special procedure to reset. On all other cars that pressure-differential valve is spring-loaded so all you have to do is fix the leak and you're done. Ford's valves are not spring-loaded and can be extremely frustrating and time-consuming to reset, especially when they get to be a few years old and that valve no longer slides freely.

As for the charging system, Ford had one of the better generator designs as far as diagnosing the system, through the '90s, but then for some reason the engineers buried the key test point so you can't get at it. The only thing you can do is measure battery voltage while the engine is running. It must be between 13.75 and 14.75 volts. If you don't have a digital voltmeter, Harbor Freight Tools has a perfectly fine one that often goes on sale for less than five bucks. Even at that price, it has a number of features I would never use as a former tv repairman. If the voltage is too low when the "battery" light is on, suspect worn brushes inside the generator, especially if it acts up intermittently. If the voltage is acceptable when the light is on, or even just a fuzz high, suspect a defective diode. Only a professional load test will verify that. The test takes just a couple of seconds. It takes longer to connect the tester's cables.

The brushes are bolted to the back of the voltage regulator which is bolted to the back of the generator. They used to be real easy to replace before they started adding covers and shields to the unit. Only the Chrysler alternators were easier to work on, often without even removing them from the engine. The same parts are shown for the newer Ford generators but I haven't worked on one newer than from the late '90s so I don't know what's involved. If load-testing shows a defective diode, it's not practical to replace that one, or a set of three. With parts cost and time, you're better off just installing a rebuilt generator.