Trouble with the blower motor
If it's not working at all, start with checking the fuse #2. Remove the lower shroud of the dashboard (secured by seven screws). A relay is fixed to the right side of the steering column. Turn on the ignition. As you turn the blower speed knob to the full speed position, the relay should click. If it doesn't, check its feed (connector #1). Then jumper its connector #2 to the ground, this time it must click. If it doesn't, it's faulty. If it clicked this time but it didn't when you have just turned the knob to the full speed position, you have to check the heater controls.
Pull free the three control knobs (take care, there is a flat spring in each of them, try not to let them fall, they have a tendency to fall through every aperture they might find). Undo the two retaining screws now exposed. Go up to the ventilation grilles, remove them carefully (use a small screwdriver as a lever on one side, these grilles also have flat springs on the sides, take them out carefully). Then look into the aperture where the grilles were. On the left wall of the left aperture you'll find a metal retaining clip. Slide the screwdriver behind it and pull it towards the center. As you do so, the left side of the center console can be pulled out a little bit. Do the same with the clip on the right wall of the right grill aperture, this time the whole center panel will come out. As you remove it, disconnect the cigar lighter wiring.
Check that pin #3 of the 5-pin brown connector is at ground level. Then check that the potentiometer formed from the printed circuit board is functioning and the wiper arm is making good contact.
If the relay clicks but the blower motor doesn't turn, the motor is suspect. Jumper the connector #3 of the relay to the ground, the motor should start in full speed. If it doesn't, first check for 12 V at the main board connector III/6 (a 6-pin white connector) at pin #1, then directly at the motor terminals. The motor is located in the engine compartment, in the bulkhead cavity just forward of the windshield. You can disconnect the wiring without further disassembly but if you need to repair or replace the motor: remove the wiper arm and spindle nut. Remove the retaining clips and prise free the rubber seal from the top of the wall between the cavity and the engine compartment, then remove the plastic covering the motor. Prise free the clips retaining the air intake grill (the one the wiper spindle is going through) and remove the grill. Remove the three retaining bolts and lift the motor out; you might find it easier to do if you unclip the round air intake grill as well. The motor housing can be separated into two half-housings after unclipping.
If the motor worked when you jumped the wire, move this jumper wire to connector #5 of the relay; the motor should stay on. If it does, check the yellow wire starting from this relay connector going through pin #6 of III/6, all three pins of II/4, finally to the grounding spot along the left side of the steering column.
If the relay and the blower motor work well in the full speed position but the lower speeds are faulty, locate the control module (a single transistor sitting on an aluminum heat sink, on the underside of the steering column; it was later moved into the blower motor housing). Using a test lamp or a voltmeter, check that the voltage present in the green wire with blue sleeve (later modules: pin #5) connecting to this module changes gradually as you turn the operating knob on the dashboard. If it does, look for similarly changing voltage in the other wire (yellow but with white sleeve; later modules: blue wire at pin #1). If the voltage is correct in the second, the relay is faulty, otherwise the transistor. The newer modules are grounded separately through a blue wire at pin #2 and connected back to the center console knob by a brown wire at pin #4, check these before condemning the transistor. Remove the module, desolder the transistor, remove the securing rivets by carefully drilling them.
Buy a 2N4399 or MJ4502 transistor at a common electronic parts store (both are manufactured by several companies including Motorola and STMicroelectronics: PNP power transistors, 60 V [2N4399] or 100 V [MJ4502], 30 A, 200 W, TO-204AA [formely known as TO-3] package). Just for the record: the original transistor was an SGS-Thompson FW26025A but this is an internal factory name and is not available anywhere, nor will SGS-Thompson reveal its true identity. The suggested replacement transistors are, although not 100% equivalent, good replacements and being components in widespread use in the electronics industry, should be easily and cheaply available. The only difference to the original transistors is a slightly lower speed of the blower motor but in the BX (unlike in the XM, for instance) the full speed bypasses the transistor through the relay you have just checked, so the actual full speed will not change.
Grease the bottom of the new transistor with silicon grease (if you omit this, the efficiency of the heat sink will be much lower, although the circuit will work, the transistor will run significantly hotter), secure it with bolts and nuts and solder its two terminals. Later BX and BX 14 models have a resistor on the module. Check and renew it if necessary. Refit and reconnect the module.