Q: Car not turning over

Started my car after a long work trip, didn't turn over. Had friend jump the car and it started fine, and ran fine. I even went to a store, came back out and it started back up fine.

The next day, however, I went to start it again and all the lights and sounds on the inside of the car went haywire (they were flashing on and off and wouldn't go away even with the keys out of the ignition), and the car would not start. This was accompanied by a repetitive ticking sound coming from the ignition, fuse boxes, and engine. Not knowing what to do I unhooked the fuses where the ticking was coming from just to get it to stop. I eventually had the foresight to just unhook the battery, which I did, and all noises/lights stopped.

Talked to a mechanic about it and they said it was likely the battery. My battery wasn't that old, but I replaced it anyway. The new battery powered everything on normally, but the car still didn't turn over. Tested the old battery, and it tested good. Thoughts?

My car has 91000 miles.
My car has a manual transmission.