1990 Buick Century fan

I'd do some testing at the fan relay. It should be in the relay pack under the hood. If your not sure which one, look at the wiring colors, at the connector.
Black with red stripe--- red-- dark green with white stripe--- brown. The red wire should be hot all the time, there should be a wiring diagram on the relay. If you use a jumper between the terminals for the switch side of the relay, the fan should run, does it?

The fan should also run if you turn on the ac.

The cts could also cause a problem, are there any codes? You would need to do some testing to find the exact problem.

www.autozone.com should have wiring diagrams for your vehicle, just click on (vehicle repair guides) and follow the links.