I would check to see if your vacuum booster has a vacuum leak, is
the brake hard to push?
If not What about the battery negative cable it goes from the
battery to the frame near the battery and then to an engine hook thing.
Try putting a big jumper from the frame to the engine and the frame to
the battery negative cable and see if that keeps the engine from almost
stalling when you step on the brakes, Maximas of that year have all
kind of ground problems with age, try soldering all those little ground
wires going to your engine.