Blower fan problems (only max speed and not turning off)

Just bought a 98 Intrigue with 53K miles. The blower fan began to act up. Issues:
1) Blower only blows at highest fan speed and only when fan speed is set to one of the 3 lowest settings.
2) When fan speed setting is at one of the highest 3 speed settings, the fan turns off.
3) Consistent with the above 2 items, when using the Auto Climate Control button, if the fan begins on one of the lower 3 settings (and is therefore working but always blowing at max output), when the display shows that the fan speed setting is increasing to the 4th-6th highest settings, the fan turns off.
4) Looked at the fuse box in the cabin and discovered that the fuse for all but the highest fan blower setting was missing. Replaced it but it did not make a difference. (I'm pretty sure I tested the various fan speeds before purchasing the car and they worked but I don't know how they could have without the fuse.)
5) Today the fan continued running after the ignition was turned off. Had to disconnect the battery to get it to turn off. When battery was reconnected, fan remained off.

Having searched forums, I've seen several possible problems.
1) Blower motor resistor. It sounds like the high/max speed does not use this resistor which is why it could still be working. (If this is the likely problem, is it possible to use a cheaper 'manual' resistor rather than the more costly 'automatic' resistor?)
2) Blower motor control module.
3) Ignition switch

It was also suggested that the cabin air filter be looked at because it could affect the resistor.

So any ideas on what is the likely culprit or some way to determine which it might be (or some other problem)? Thanks in advance.

If you have auto temp, you have a blower module, not a resistor block.....

If the blower stays on, usually a bad module......BEWARE.....a spiking blower motor can take out a new module,,,,,

In auto temp, blower speed should not be constant.....it should vary....for example, if the car is a little warm, and you turn the temp selector down, the blower speed should increase with cooler air out of the duct......then if you turn the temp selector upward, the speed should decrease as warmer air comes out and the the auto temp system has reached it's goal....

In MANUAL mode, the blower speed should remain at whatever you set it at......

Thanks. Would a faulty module also explain why the fan only worked on high speed for lowest 3 speed settings and turned off for highest 3 speed settings?