03 cadillac escalade speedometer will not work

Scan the vehicle for fault codes first. Sounds like you need to check the vehicle speed sensor signal into the speedometer. If that is ok then send the speedo head out for repair.

GM used a bunch of "stepper motors" in the dash cluster in this and many other vehicles in this time that were prone to failure. Speedo, Oil pressure, Temperature, Gas gauge - you name it - they were all the same stepper motor.

You can replace them yourself for short money - but you need soldering tools and skills. It's a great time to replace dash lamps, too. Check out eBay for parts.
Escalade Speedometer eBay

And this video to learn how to do the work:

Chevrolet GM Speedometer Gauge Repair Removal Instrument Cluster

You are correct in thinking if the speed sensor fails the check engine light should be on, and you should experience problems with the transmission.
It sounds like just the speedo has failed.

This is a common problem with gm speedo's. You will have to get it rebuilt. You can find these on ebay rebuilt and ready to go in your vehicle.

Scan the system for fault codes, you could have a defective speed sensor or a defective speedo both are possible.

lol...either a map sensor or the throttle body sensor....

speedometer drive gear stripped or cable binding

The speedo head or cluster is the part that houses the speedometer and tach, etc. now it may be the speedo cable that comes from the transmission to the speedo head that has broken. If so replace the cable and your back in business. If it is the head you can get them from your local recycle yard.

replace the cluster

the little motor that moves the speedo needle is defective, u will need to send the speedo out for repair at an authorized factory repair center like the one in the link below.
http://www.dnaspeedometers.com/