1993 Honda Civic Honda Starts Intermitently

My Civic started great this morning. I planned to take it for some exhaust work because of a leak before the catalytic converter. When I arrived at the mechanic, they were closed and the car would not start. By this I mean nothing happened when I turned the key - no lights, no radio, no cranking of the engine. I played with the key for a while and the lights would come on only half the time.

I tried a push start (car in neutral, pushing for forward movement, the popping the clutch) since that has worked in the past when the battery was bad. Nothing happened. Then, I tried to start the car again. This time everything turned on like it should and my Civic started right up like it did earlier in the morning, so I drove to work. One thing I noticed on the way to work is that the power had been completely shut off - the radio had reset itself (station presets and clock), so I am assuming the problem is electrical.

After parking, I tried to restart the car, and the same thing happened - absolutely no power to anything.

Thanks for any help!