2005 Honda Civic Car runs for a while and then goes dead at

Electrical problem
2005 Honda Civic Automatic 75K + miles

She used to run great. And then one night, driving around 75mph down the freeway at night, with the lights, stereo, and heater on, the ABS, E-brake, and passenger side airbag lights came on. Thank goodness I was close to my destination, because I got worried. I reached my exit and used the turn signal, but the light was very dim and erratic. I had no steering/braking problems all the way to my destination. When I went to start her up later, all of the lights on the dashboard flickered and the engine turned over but it didn't connect.
She works when forced, when the battery is jumped. Since this first started, I've had the battery and alternator replaced, oil changed, etc. She will run during the day, but it seems to be that at night, with all of those things running [lights, stereo, heater/ac, etc] that her battery grows too weak and she doesn't start the next time I try. The auto shop I'd been taking her too says they can't do anything about it because if those lights don't come on while she's at the shop, they can't diagnose the problem. It's been driving me crazy, and I've been bumming rides for a few months now. Somebody please help.