Very odd set of issues involving start up, Battery wont have power sort of. Options

[HaysoosKreesto]

Well... ok so, my 98 recently had two episodes that would seem as if the battery would need to be replaced.

1) Was at a park, and the car was still warmish from a fresh drive and it wouldn't start. The odd thing is that when I tried to turn over the engine, all of my lights on my dash died and nothing started. When I got a jump I noticed that my dash clock and stereo clock were forward by 20 minutes and the battery ran the whole drive and several days afterwards absolutely fine with no problems at all. This was the first episode.

2) After work today, the car was cold because it was off for 5 hours in the cold. Once again, the lights on my dash were fine upon key entrance but when I went to turn the motor all the lights died and the battery needed to be jumped again, however, this time both clocks were forward by 2 hours... Once again, after the jump the battery will drive just fine with no signs that it needed to be replaced during the drive (I mean like no dimming of anything, the headlights seemed normal, and no odd sounds).

I'm guessing that my battery is probably either the incorrect size, or hopefully this will never happen again. So I guess my main question is =>

Has anyone ever experienced a dead battery and time shift?