Strange electrical drain w/flashing headlights

[titanneil]

O.k, here goes...
I just bought a 2002 Windstar, knowing that it had some issues to be resolved before putting it on the road (yes, the van was quite cheap). First off, the owner said it needed an alternator, since he had replaced the battery 2 months previously and it would not hold a charge.
We charged the battery up last Wednesday, and it fired right up. I could hear the vacuum leak in the intake manifold (2nd reason it was cheap) but ran ok. All seemed well, with 12.9 volts on the battery and the alternator putting out 13.3 (tested on back of alternator, grounded to body). I'm no electrical whiz, so let me know if i'm doing something wrong.
Went to get the van today (Sunday). Hopped in and cranked it over, fired right up and seemed fine. After letting it start to warm up for 4 or 5 minutes, the battery light came on and it started to idle a little rough. I turned off the ignition, then went to start it again - only to have it click, click like the battery was dead. Evey warning light on the dash was on, amd when I took out the key, there was a dinging like I had left the headlights on. Well, they were on, only flashing! The headlight switch was off, everything was checked twice, in the end I had to pull the negative lead off the battery to turn off the headlights. Very weird.
Went back to the van later today with a new megafuse in hand, thinking there was a problem with the 175 amp fuse which could be causing this (read a few posts about this on other sites). Could not locate this fuse on the van, it appears to be a fusible link only between the battery and alternator.
I cleaned the corroded battery connections and put dielectric grease in there, tested the battery voltage (13.3???) and turned the ignition on -same clicks. The battery voltage was dropping fast on the meter, probably a volt a minute if I left the ignition on.
What could be going on? The battery sat for 4 days without draining, but 4 minutes of running killed it? Then it 'recharged' to 13+ volts on its own, only to not be able to start the van again?
My guess would be that the battery is not discharged, but something is seriously draining the voltage when the ignition is on. Ideas?