best action for partial removed alarm

Facts:
-2003 Jeep Wrangler 4.0 5sp Sport
-PO had an alarm and remote start installed. It appears to be a base model alarm by the tiny cheap looking plastic siren, but I am not a pro.
-Story is her mother disagreed with remote start on a manual, so her mother took it to the dealer(I'm thinking Jeep dealer not alarm dealer) to have it un-installed.
- I own the Jeep now, the door chime goes off any time the door is open whether or not the key is in the ignition or the lights are on.
- Auto locks lock the doors after start up and unlock them after the key is removed
- light installed into dash never lights up.
- clutch is not needed to start the jeep - I actually like this:)
The problem
- The constant door chime is a major pain in the butt when cleaning, maintaining, or using the jeep.
- My ability to tune-out the door chime has led to leaving the lights on. Now that I am going backcountry skiing this could really be a problem.
- The autolocks and are okay for hardtop driving, but unnecessary and an extra step when the top is off. I leave the jeep unlocked.
-The current installation has no connect/disconnects for the wires to the door locks. so I cannot take off the doors?

My Question(s)
1. Would returning the door chime to original working order be a simple DIY fix or a job for a pro? I am low skill, I can install head units and amps on easy cars as long as it doesn't involve soldering, but have never even looked at an alarm. Is it as simple as looking for a connection to a wire or replacing a fuse?
If not,
2. With the work you imagine has been done so far to install that alarm, would I be better off to:
Have everything uninstalled by a professional
Have the unit re-activated by a professional and buy new key fobs.
Have a new unit installed the way I would want it?

Basically, If I pay a pro for the time it takes to remove the system correctly and completely, would it be the same or more as the labor to install a nice alarm.

I am sorry for the lengthy post, but I wanted to make it easy to answer.

Thanks in advance

I can't get my head around the door chime operating all the time which is why I would go for a pro looking at it and giving you a price to make it work.
I can't see how the door chime would be any different with either the alarm on or off unless there's a bad connection to the vehicle key sense wire.

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Amateurs assume, don't test and have problems; pros test first. I am not a free install service.
Read the installation manual, do a search here or online for your vehicle wiring before posting.

As Howie already pointed out, if they grounded the keysense wire, this could be the cause of the constant door dinger.
     Key Sense          LIGHT BLUE          (-)          IGNITION SWITCH HARNESS

Some vehicles require the keysense wire to be activated so it thinks a key is in the cylinder. Most remote start units have accommodations to do this only while under a remote start situation. Your unit may have not been able to do this and they had to ground that wire.

I will look for that wire. Thanks.

And, would they have done something that could also affect tge way the clutch and brake turn off the cruise control? Is there a clutch switch that has to becdeactivated for remote start? My brake and clutch do not turn off tge cruise when pressed.

Probably the same reason though I must add that pro installers would or should never leave a vehicle like that, OEM functions should/must remain unaffected.
Get a pro to completely remove and restore functions, although I think the basic problem is probably a bad ground on this unit, hence it's grounding out through everything else.

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Amateurs assume, don't test and have problems; pros test first. I am not a free install service.
Read the installation manual, do a search here or online for your vehicle wiring before posting.