1992 Cadillac Coupe Deville blower fan runs all the time

i will now read the online service manual to you.
https://eautorepair.net/Marketing/Default.asp

blower fan located where. dash heater blower fails
or radiator fans of some odd kind added later.
coolant fan or dash? there are 2 coolant fans and 3 relays to run them and all 3 relays, can fail and coolant fans blow for ever and ever. fuse 6 kills the relay coils. only, so if relay is welded fans blow endlessly. even if bcm is removed from the car.
on the other and the heater blower is 100% controlled by the BCM

so car engine starts and runs and drives ok right.
when did car last run perfectly> , or seen ever ?
service manuals for 88 cars are not easy to find
means real oem manuals, best. 35 years old !
no digital then ,just a huge paper bound book, remember?
holy moly this 88' has a body controller here, bcm , relic amazing thing.
facts: 1988
here is proof

Are you sure it is the AC blower? a lot of modern cars have a temperature controlled radiator fan, this can run when the engine is very hot , even when the keys are removed. It is a safety feature to protect your engine.

it is in your defrost controller,believe it or not when your defrost is turned on it engages your a/c pump.it all in your dash controls and not a hard fix even in a caddy

You need to replace the blower resistor. In should be in the blower housing under the hood.

blower motor,relay fuse

Ralph,
Most common cause of this is the blower fan (proper name for the fan you refer to) continuing to run is a shorted out Electronic Climate Control Module. This solid state device replaces the older style fan speed resistor block (at about 4 times the price) This unit is found on the top of the HVAC box under the hood. (HVAC means heating, ventilation and air conditioning) The HVAC box is found on the passenger side of the firewall. Look behind the A/C's accumulator. It will have an electrical wiring plug on top of it. It will be fastened to the HVAC box with a few 7mm hex head screws. Very easy to change.
FYI, do yourself a favor and replace the blower fan motor at the same time. The Electronic Climate Control Module usually fails because the motor is drawing to many amps of current. This is because it's bushings are worn out or the brushes are worn out.
This is very common on Cadillacs and Buicks.
Charlie
PS Not sure why car won't start. Either you drained the battery or blew a fuse which controls starting the engine. Need more info regarding the "no start" condition.

It has a blower control module instead of a resistor mounted in the box next to the blower motor. The blower control module is bad

You checked the fuses, that's a good place to start. Usually electric fans are powered up using a relay. It's likely that each fan has it's own individual relay so it's strange that niether fan works. Is the engine overheating? Try turning on the air conditioner after starting the engine. One of the two fans should definitely turn on immediately after switching on the A/C. If so, then the other fan, which would be controled by the temp sensor circuit, might be bad. Before replacing anything you may want to check the temperature sensor is working properly. The relay(s) are probably located in the engine compartment usually near the firewall. Hope this is helpful, if so, please remember to rate my response. Thanks.

replace the relay , when a relay sticks like that , a good test is to slap it with something like the handle of a screw driver , see if it un-sticks , its not a fix , just a test . cheers'