Cadillac cts cranks, sputters a little, but won't start.

This link had your same problem last comment may help
https://www.cadillacforums.com/forums/cadillac-cts-first-generation-forum-2003/414449-cadillac-starting-problem-after-serpentine-belt.html
This link had your problem and found a solution
https://www.cadillacforums.com/forums/cadillac-cts-first-generation-forum-2003/890066-car-wont-start-after-replacing-serpentine.html

Temperature sending unit could be sending erratic signal.

junk the caddy ,

Don't do that again! You will need to re-boot the on board computer system by entering a code. Call your nearest Cadillac dealer.

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You should be able to start, what is the fluid level bring it to the recommended level crank it allow the lifter to solidify and compression will build up

Could be your cat is clogged up

it could be your starter,or it might be the ground wire from the alternator to the body causing the problem.

sounds like you will have to replace the ignition module which is where all the plug wires attatch to the coil packs.

My 2003 CTS would not start on the first, second or third try after filling the gas tank. Finally after several months of this occuring every two weeks a check engine light came on. It was the evac purge valve. Tom

Sounds like your alternator is not charging your battery. Probably a loose wire, battery cables, alternator wires, or possibly a bad alternator. Check all the wire connections. Check for a loose or bad alternator belt and have the alternator and battery tested.