1998 Honda Accord Dash lights remain on

Recently when I started my Accord, all the system lights on the dash came on, including the SRS, Brake, "Doors Open" display, Eng, Maint, etc. They still remain on after approx 500 miles of it being like this, but will occasionally flicker off. Very annoying at night. I read on a Honda forum that it could possibly be a bad ignition switch.
Also, don't know if its related, but at the same time, my battery started draining overnight. After a few mornings of untangling jumper cables and boosting off my wife's minivan, I now just disconnect it at night and reconnect in the morning, and it starts fine. I had the battery/charging system checked and its came out ok. A friend told me that if the terminals on the back of the alternator are magnetized with the car turned off, that could be causing a slow drain. I checked and they are strongly magnetized. The alternator is about 2 yrs old (remanufactured).
Question: Is this 2 different problems? They both occured after the car was rained on for a couple of days. Otherwise, this car sits outside all the time and had no previous problems and has been very reliable. Any help is appreciated.