Battery light stays on until I accelerate, but comes back shortly after

I have had this issue for the last three days, until today when the battery finally quit running. As stated, the battery light would come up while driving and stay on until I accelerated, but would come back a few moments later.

On my way to work this morning the radio would flicker off and on until quitting for good shortly before I made it to work, where I found the battery to have died.

The connectors are clean, I have yet to do a load test to see if it is putting out 14 volts. I recently replaced the spark plugs, wiring, and torque converter. Could it possibly be a problem with my PCM? Or am I out for a new alternator/voltage regulator?

Update: went to check on it during a break and it cranked up no problem, maybe something shorting? We have had a great amount of rain here the last month.

Okay, I put my meter across it after cranking and read 20 VDC. I then left it idling a few minutes, shut it off, then tried re-cranking, no luck, but I noticed the needles in the cluster started jumping slightly, even when the key was turned to off.