When should a serpentine belt on a 2004 CTS be replaced?

Two, one does the AC

https://www.gmpartsonline.net/v-2004-cadillac-cts--base--3-6l-v6-gas/cooling-system--belts-and-pulleys

and also

https://www.2carpros.com/diagrams/cadillac/cts/2004

..

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

The proper terminalogy is it crank's but doesn't start an run . A crank no start condition . What's missing , spark or fuel ? Do you know how to test for these ?
No Start Diagnostic Basics EricTheCarGuy

The same thing happened to my 03 CTS. The camshaft position sensor code is often thrown for a variety of reasons. In my case somehow the ECM went when the timing belt jumped (after the serpentine belt broke). It was a bear to diagnose but after installing a rebuilt ECM it runs great. (Don't make the mistake I made: the cylinder head gaskets will fit nicely on either side but if not placed on the correct sides you'll block the single oil port which provides engine oil to the head)

Below is the master help link provided to go through belt routing diagram:---Timing belt, drive belt, serpentine belt, accessory belt, fan belt, engine belt routing diagrams for all types of car models?
Click the link below: ----

http://carbeltrouting.blogspot.in/2012/02/timing-beltdrive-beltserpentine.html
----------This will help. Thanks.

re-check the belt routing sounds like the belt is not routed correctly

I hope this help's you, good luck.

I aassume you are asking how to change your serepentine belt. Follow this link to a video series which explains how to change it...

http://www.wonderhowto.com/how-to/video/how-to-change-a-serpentine-belt-on-your-car-39904/

You'll need a diagram of the belt routing so you can put it back on correctly...

you bent a rod get the motor from someone other than dealer they will soak you

There is a belt routing sticker under the hood, other than that and a few hand tools there is a problem to replace this belt.