No fire

First of all, I see the 2006 Cadillac DTS had a 4.6l engine, not a 4.3l.
Second of all, check your fuel injector fuse/s.
If you have any starting fluid, see if the engine will start and run for a few seconds after spraying a few shots of starting fluid into the throttle body.
If so, the ignition is fine and might be no injector voltage or no pulse.
If the fuel injectors do have voltage to them with the key on run and start then you may have either a blown PCM fuse or a faulty crankshaft position sensor and/or wiring, but I doubt that cause of no codes.

It is at the front of the intake manifold, shown in this diagram with a large round opening. You may have to remove the air cleaner in order to spray starting fluid into it, but if you do smell gas and it is still not starting, plus no codes meaning the ignition is working, then most likely the spark plugs are gas fouled. Remove one and smell it, if it has a strong smell of gas, they most likely they all do, so remove them all and clean them off with some carburetor cleaner or that starting fluid, allow them to dry for five minutes or so and put them all back in and try again.
Unless you want to confirm first of all that you do have spark on at least one cylinder.