88 Cadillac Deville cooling fan runs continuously

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

it will do it will keep going till engine cools its surposed to do this it will shut when its cool , if it still does it after its cool then u need to replace temp sencor it on side of rad

You need to find out what is missing when it won't start , spark - ignition system or fuel pressure . No Start Diagnostic Basics EricTheCarGuy

REPLACE THERMOSTAT AND RADIATOR PRESSURE CAP.MAKE SURE COOLANT NOT LOW.IF ALL IS GOOD CHECK FOR LEAKING WATER PUMP WEEP HOLE IF LEAKING REPLACE WATER PUMP.MAKE SURE COOLING FANS RUNNING.IF ENGINE RUNNING HOT WHILE SITTING LONG TRAFFIC LINE AND COOLANT NOT RUNNING.CHECK COOLANT FAN RELAYS AND FUSE.IF ALL IS GOOD HOT WIRE MAKE SURE COOLING FAN MOTOR GOOD IF COOLING FAN DONT RUN WHEN HOT WIRED FAN MOTOR BAD.IF FAN MOTOR OKAY AND FUSE RELAYS GOOD YOU HAVE FAULTY COOLING FAN WIRING.YOU COULD HAVE BAD ENGINE COOLANT SENSOR OR FAULT IN ECM CODE SCAN TO CHECK THEM BOTH.CHECK ENGINE OIL.LOOK LIKE MILK SHAKE YOU HAVE LEAKING HEAD GASKET.IF OIL LOOKS OKAY.YOUR ENGINE BLOCK, RADIATOR AND HEATER CORE NEED FLUSHING.

Possibly in a "Safe" or "Limp home" mode. If so, have a look at the wiring harness on the transmission. I'll bet that the seal around the lid on it is failing. Clean the harness up, and reseal the lid on. If this does not fix it, have a mechanic look at the shifter linkage.

faulty fan relay?

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.

try at your local auto parts store and see if they can order you a Haynes manual for your car or google the manual for your car.

Try unhooking the battery. These are good for setting a false low coolant code in the computer and shutting the whole system down.

Replace tank sending unit an the trunk pull down switch. See gm dealer for diagrams!