I have a 99 Grand Am SE that has just this week developed a problem
starting after long (6 hr or more) periods idle.
The vehicle will attempt to turn over, but very slowly, and the car
will not start.  The dashboard indicators will come on when I turn the
key, and sometimes the trunk will even open, leading me to think it is
an electrical problem.

The first time this happened, I could not get the car to start at all,
despite several minutes of trying.  Even though it was acting like the
battery was dead (except for the dashboard indicators and the running
lights working), I knew I had not left anything on overnight, and I
was not getting the low battery indicator.  I had it towed to a
garage, and they were not able to find a problem.  They tested the
battery and it showed a 96% charge.  They were able to jumpstart the
car, and it started fine for them after that.

When I went to start the car next morning, it started, but hesitated
just slightly before it did so.  This morning, the hesitation was a
little longer.

This evening, I tried to start the car, got the slow turnover, but no
start.  After trying for a couple of minutes, it started, but the
clock had reset itself, as if I had just had the car boosted.  When I
got it home, I shut it off, then tried it again.  It started right
away.
It's a fair bet that when I try to start it again tomorrow, I will
again have problems.

In short, it's acting like it's got a run down battery, but nothing's
left on in the vehicle, so I think the problem may be something
electrical.  From all I've read, the 99 is prone to problems like
this, but there does not seem to be any consensus on cause.
Can anyone suggest a cause for this, and a possible solution that's
not going to cost me more than the car did?

Thanks.