2001 Acura RL Car wont stay off

Electrical problem
2001 Acura RL 6 cyl Automatic 93000 miles

Started last night. Noticed windshield wipers on in car. No one in car. Car not on. We had been home about an hour and I was using them while out. But the car was OFF. No key. This morning car COMPLETEL DEAD. Cant even jump it dead. Went and bought new battery. Car started fine. Go back out to car 20 minutes latter. Entire dash board on like key is turn half way on in ignition, but no key in the car. Car SHOULD be off. I got the key and started the car. Turned it off. Dash wont go off. I started it again and drove around the block. Came back and turned it off. Everything appeared o be off this time. Had my husband disconnect the battery for tonight so as not to kill the new one. I see now that the old one was probably not bad just drained because something came on in there and probably stayed on all night. Never seen anything like this in my life on ANY car. Do you have ANY clue what could cause the car to turn its self on?
No I don't have an auto start. I bought one and never had it installed.
AS far as I know there is no after market alarm or anything on the car now.
Only other problem I have had is: I noticed that the factory clicker for the door lock doesn't tut the horn anymore and sometimes acts a little funny. Couple of times it wouldn't work at all then started working again, it isn't facially damaged so I figure it just needs a battery, And water getting in the car through the cowl under the top of the hood near the windshield. The guy at Glass Masters said the galvanized rubber gasket that should keep water out is warn and shrunken from heat but the tape he put around the air vent where the water was coming in at didn't work. Been leaking again lately and we just had massive rain week. But this has been there for over a year. Never caused any problem except when it rains water will come in and run down on your feet.
If you can give me a diagnostic that will save me hours of UNGODLY charges at the dealer I will GLADLY make a healthy donation I PROMISE. I am SCARED right now. HELP!