Those type of drip brewers generally have a sensor in the "boiler" section. Normally when water is flowing the boiler will be "X" temp (ideally about 204f for a good machine that meets SCAA specs), when the tank runs dry the temp in the boiler will rise to about 212F which is how it knows that the brew has finished.
Sounds like
@BillW50 either has a clogged tube going from the tank to the boiler, restricting water flow and allowing the boiler to "boil", or a clogged tube from the boiler to dispensing head, restricting flow out of the boiler thus allowing water to remain in the boiler too long and actually come to a boil.
@awsum140 suggestion of running vinegar is a good one. Also check the tubing coming out of the boiler, it may have gotten kinked.
If the above doesnt work then you probably have a bum sensor. The sensors in those things can be bi-metal metallic, thermistor, RTD, Semi-conductor (not likely), or thermocouple depending on the quality of the construction.