Rep Power: 0

I have a 2005 Civic 1.7L DX. I went to start it in the morning and something was winding but the engine wasn't turning over. It was definitely a different sound from the starter freely spinning, and it kept going for ~3 seconds even after I took the keys out of the ignition. It then started up, but for the first five minutes of driving the lights would flicker every 30 seconds or so, coupled with the radio resetting. About 15 minutes into the commute I was on the freeway and everything completely died like the flip of a switch, couldn't even turn the hazards on. The AAA guy tested the battery and told me it was overloaded, was making his leads hot to the touch.

My mechanic thought it may have been something that went wrong with my starter, based on what happened when I first started it, which somehow eventually fried my battery. I replaced the battery and the starter and it seemed to fix it until the next day (today). I got to work just fine, went to fire it up at lunch and it wouldn't turn over. The mileage readout showed "Trip AB" fully illuminated and the numbers 888888888 flashing (they were alternating between 0 and 8 randomly). Checked the battery and the voltage was fine. I noticed the positive lead had a lot of buildup, so I cleaned it off and now it starts again. Was this all as simple as corrosion on the lead? Based on the way it started funny the first time, the sudden blackout, followed by spells of working then not starting makes me think it is something more.

 
Rep Power: 223

What does the battery voltage read while the engine is running?

Check and clean all the power/ground cables.

 
Rep Power: 0

14.3 V when running. I just took the battery off to make room for replacing the water hoses and thermostat and found that there was a lot of build up on the positive lead considering I cleaned it a month and a half ago.