5000T has trouble starting

[gooley@netcom.com (Mark. Gooley)]

My '88 5000T over the past few weeks has had trouble starting, and
the engine is prone to die shortly afterwards.  Last Thursday (on a
fairly hot and humid day) it would not start: sort of a half-hearted
ticking noise from the engine compartment and a trilling beep accompanied
by a fast, dim strobelike flashing of the warning lights on the panel.
I waited a few minutes and the car started reluctantly.  In the evening
the same sort of refusal to start; after a dozen tries or more the battery
seemed to be near discharged.  I got a jump and the car started perfectly.
Since then it's tended to stall shortly after starting, but otherwise it's
back to normal.  Any ideas of what might be wrong?  It still has the original
battery -- could that be it? (But the battery warning-light doesn't light
up, except in concert with a lot of others during starting.)

Mark.
gooley@netcom.com