Seville completely dead. Will not start.

[llkeith]

I have a '96 Cadillac Seville SLS with 75,000 miles. The car has run great for me until recently when I parked it for a short time then came back out and tried to start it. It would not start, even with a jump from a friend. The next day I changed the battery and the car started and ran beautifully.
Yesterday after driving my friend to the airport I stopped in at a gas station and returned after a few minutes to find the car would not start again. No interior lights, no dash read out - nothing. Someone tried to give me a jump, but to no avail. After I sat around chain smoking for 30 minutes the interior lights and dash display suddenly came back on and the car started perfectly.
I drove home and the next day I took the car on several short trips with no problems starting it. The voltage readout indicated the battery was running at a constant 13 volts.
When I went to start the car this morning the keyless entry worked and the interior lights came on when I opened the door. Everything seemed fine. Then everything went dead again. No lights, no dash display. No noise whatsoever when I tried to start it. Unlike the last time, the interior lights have not come back on and the car remains completely dead.
Of note, the most recent cut off of all power occurred immediately after I placed my iPod into the car dock (which is connected to the cigarette lighter). The first two times I had left my iPod on when I shut my car off. Not sure if that matters, but please help.

[maxwedge]

I'd start looking for a bad ground or pos cable connection at the battery, chassis/engine ground, or pos cable to junction under the hood.