1996 Maxima, shift stuck in Park position

It is locked several ways.

There is an electrical interlock that is activated by the brake pedal when the ignition is on. Check that the switch on the back of the pedal is working.

There is also a mechanical shaft running to it from the ignition switch that could be sticking.

There is a solenoid mounted at the base of the shift lever that pushes (pulls?) the interlocks away. They get weak or gummed up (Pepsi syndrome - have you spilled anything in there lately).

To test, pop off the trim plate around the shifter (I have good luck using an old putty knife wrapped in an old t-shirt. Start at the rearmost corners and work your way to the front. It should have about 6 snap clips and hooks under the trim around the ash tray. It should pop out.).

Once you have the cover off, look at the base of the shifter on the right side and you should see the solenoid. It has a shaft coming from it that connects to a pivot at the front right side of the shifter mechanism. The shaft coming down from the ignition switch comes into that same pivot from the front.

Turn the key to run and step on the brake. The solenoid should move the plate on the pivot out of the way and the button on the take-it-out-of-park button should be free to move. If nothing happens, try moving the pivot by hand (or with a screwdriver if your fingers are too fat to reach down in there (like mine). You might need to also remove the ash tray to reach it. If it is gummed up, try to loosen it up with WD-40 or something similar that will not turn sticky itself. If that fixes it, you are done. Otherwise, replace the solenoid. (about $70 from Courtesy Nissan).

Meanwhile, until you get it fixed, leave the trim plate off and keep the screwdriver handy so you can push the stopper out of the way manually to get the shifter out of park.

The very first thing you should do, with respects to e.meyer, is check the fuse for the brake lights. I forget this everytime I buy a new Nissan (or Infiniti) SUV and hook up my trailer; the factory fuse cannot handle the extra load of the trailer lights.

Its always a good idea to check the related fuses when anything electric stops working, but in this case, if it sometimes releases if the OP jiggles it, it can't be a blown fuse - jiggling things can't make contact through a blown fuse.

I've never seen anybody tow anything with a '96 Maxima though, so who knows what problems that could cause?