I have a '95 850 GLT at 105K with a strange electrical problem. Sometimes when I put the key in the ignition and turn it, the doors lock and then the car won't start. If I take the keys out, then _sometimes_ the alarm goes off. I've always been able to get the car to start eventually but it seems like every time I have to do something different to get it to work --take the key in and out a few times, get out and lock/unlock the doors, or fiddle with the headlight dial.
These problems started when the winter rains started this year, but the problem now occurs intermittently in dry weather as well as wet weather. The fuses all seem fine, no moisture or corrosion.

Other symptoms/events that started around the same time:
--sometimes gas cap door won't unlock
--backup lights stopped working -- both bulbs and fuses are fine
--"bad bulb" dashboard light sometimes comes on when I brake, but both brake lights are working
--gave someone a jump -- just connected cables to battery terminals



Any ideas?