Look behind the glove box. under dash.
maybe your blower motor relay is stuck or burned together ???
A bad heater blower motor resistor would effect one or more blower speeds other than high.
The Mercury Cougar blower motor is located on the firewall in the engine compartment. The blower motor can be seen on the passenger side of the firewall.
location of relay blower motor 1997 Mercury mystique
Under dash at RH side, mounted with 3 bolts. R&I about 3 minutes.
front of the motor
No repairing those blower motors, replace it with a new one.
If your blower is working on some speeds but not all, more than likely the problem is a defective Blower Motor Resistor Pack. The switch rarely goes bad. Just a thought.
Without knowing what model year the questioner is referring to...Budget somewhere around $35-60 for a blower motor - likely to be closer to the lower endSee "Related Questions" below for more
Remove the wiring harness from the back of the blower motor. Remove the fan from the front of the blower motor. Remove the blower motor retaining nuts. Reverse the process to install the new blower motor
Remove the glove box and the blower motor can accessed.