[ImperialCrown]

You may find helpful diagnostic fault codes stored in the TIPM, cluster (CCN) and driver/passenger door modules (DDM/PDM). You might need a special code reader to access these; like the StarScan/StarMobile/WiTech (or equivalent).
The pulsing odometer display sounds a lot like a poor ground or power connection to the cluster. A poor connection can leave a module turned on and discharge the battery. Any underdash or underhood work done to install the Remote Start should be checked over carefully. I have seen some real aftermarket accessory hack/splice wiring jobs. Any aftermarket security/alarm system?
If you do take it to a dealer, have them update the software in all the modules to the latest and greatest versions. I can check later for any TSB's or STAR case histories relating to these issues.

 

[ImperialCrown]

Update: No TSB's concerning these issues were found, except for some MyGIG radios built before 2/8/2008 could have an excessive key-off draw.
Need fault codes for best diagnosis. There were numerous software enhancements for multiple modules.
Have you done an actual battery draw test and what did you find?
By liftgate lock not working, do you means the power liftgate lock itself or the power liftgate doesn't raise or lower?
The horn is controlled by the TIPM, as is much of the electrical problems you are having. I'm not saying that it is the TIPM itself at fault.

 

[Bob Lincoln]

Sounds like the Body Control Module is misbehaving. I'd suspect the connections to it, maybe water got into the plugs as often happens.

 

[chuzz]

I agree with Bob. That BCM is the first thing I'd be checking if it were mine. It should be located under the passenger side kick panel. Disconnect your battery ground cable and then try unplugging and plugging the connector several times. This will help sweep the contacts clean of any corrosion. Or, if you can see any corrosion on the connector pins in the plug, get some electrical cleaner in a spray can and clean the contacts.

 

[browens1534]

Had an aftermarket remote start placed in between the possessed car and lock issues occurring. Had it removed, it just happened less with the wipers. Likes to almost always have a labored start on the first try.

That there was the problem. Aftermarket remote starts if not wired correctly will fry your BCM...

 

[ImperialCrown]

The 2008+ (RT) minivans don't have a BCM. All interior functions are handled by either the front door modules, HVAC, seat or CCN (cabin compartment node; which is basically the instrument cluster).

 

[merkurmaniac]

Might want to see my post on can-bus diagnosis on my 2008 Chrysler T&C. I was also at the about to set it on fire stage.

 

[John Wood]

As a side note to the above, make sure your charging system (i.e. alternator) is functioning properly under load. I had some crazy things happen when the alternator started to go including flickering odometer display, mystery windshield wipes and an ABS light that would flicker periodically. Once I did a thorough test on the alternator under load, I found that the charging voltage would begin slowly dropping. The unit would charge fine in the driveway while idling. In my case, I just replaced the worn brushes in the alternator and cleaned up the commutator rings. All my problems went away after that. I know your vehicle is much newer, but a bad charging system will cause issues on all cars with electronic computers and controls.