Suddenly Lost Power

I really need some help getting my car back on the road before it gets too cold. Recently, I had my battery go dead. I replaced the battery and drove the car for a couple of days, and the battery went dead again. I then replaced the alternator and had the battery charged. All went well for about a week. A few days ago, I pulled the car from the garage and washed it. After getting ready for work, I got in the car and NOTHING. There was no power, no click of the starter or anything. The lights wouldn't even come on. I thought the battery had gone bad again, but a test at the store said it was fully charged. I reconnected the battery, and the lights came back on. I then replaced the starter relay, which I saw was burned-out. When I turn the switch, the starter clicks one time, but that is it. The store tested the starter and said the bearings were going bad, but the motor was running. One thing I've noticed is that when I turn the switch, if the headlights are on, they go out. I have to push the lever back to the off position and back to on before they come back on, sometimes having to push the lever on and off several times. I checked the firewall and replaced what looked like bad wires, but I still can't get the car to turn over. Anybody have any idea what I should check next? It's just getting too cold to ride my bicycle.