How do I fix faulty alarm system. No mechanic, dealer, etc. can find problem.

What is your question?

One day alarm went off for no reason. Discovered it does that when car is locked. Then a day or so later the dome light wouldn't work properly. It stayed on. Now I have to turn off radio and close windows before I turn off engine or can't do it. I've taken it to a number of service stations and several dealers and no one has been able to find the problem. Could it be alarm fuse? Any other suggestions? Thanks.

What makes this problem better or worse?

Locking the door

How long has your 2006 Saturn Ion had this problem?

maybe 6 months because no one can fix it