Heater blower fan does not work

My 1999 TL did the same. The Problem was that the connector at the blower housing had overheated and partially melted. There is a TBS for 99 to 03 TL's on the blower harness. Mine had been done but after 10 years and a bad design it still happened. If this is the case a trip to the local junkyard will get you a splice with a good connector & blower. Or take it to the shop with this info.

Hello,

The blower fan can be inoperative due to a bad relay, wiring, or a faulty motor.
First check the relay, it is located in the under-hood fuse box (see diagrams below).
Check for any corrosion or burnt pin(s).
This relay can also be tested.

Here is a helpful guide:

https://www.2carpros.com/articles/how-to-check-an-electrical-relay-and-wiring-control-circuit

If the relay is good, check to see if there is power to the blower motor harness. If there is power at the harness, then the motor is likely bad. Be sure to check for any melted connectors at the blower motor.
The blower motor is located under the passenger side dash.

https://www.2carpros.com/articles/blower-fan-motor-works-on-high-speed-only

I have attached diagrams for your reference.

Please let me know if you have any questions.
Thank you.