push button heater switch stopped working

Fans fail much more often than switches. If lights come on it is even more unlikely it is a switch problem. Most likely you need a new fan motor. Was it making noise before it failed. They don't always, but that would also be a clue.

My apologies for my previous answer. I missed the fact that your car is an 88 with push button electronic controls. It could indeed be the control/switch unit that has failed. I believe it is a simple repair and replaces as a module. Google it. Try to find a used one if you can. A new one is likely to be expensive. Also there may be a blower motor resistor in your system which controls fan speed. They also fail from time to time. You'll have to google to find location, but its down by the blower motor somewhere. I just had to replace mine in my "03. First I lost all my low speeds, then finally high speed as well. You can probably do it yourself, and the part is not expensive.

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