2000 Honda Odyssey won't start in the morning
 

We have a 2000 honda odyssey with 100k+ miles on it that has a
worsening conditioning trying to start and drive it in the morning.
This was a minor annoyance this summer and fall, but now that winter
has arrived, its gotten worse. Heres the deal:

In the morning I start the van up, it starts for a moment, then stalls
out. It will not start after this, it cranks, but never turns over.
Not until I open the gas lid and unscrew the gas cap for about 5-10
minutes. Then, I put it back on, and try starting it again. Now it
will start, but there a lot of dashboard lights on(engine, brake,
traction control, etc.). If you try and drive it, it will go only
about 10-20 mph like it has no power. You can floor the gas pedal and
get nothing. From here just shut it off, and wait another 10-20
minutes. Now it will start, and everything is fine! no lights, no
problems, you're good to go for the day. You can drive it work, and
that night it still starts fine. The next morning the problem starts
all over again.

We have taken it to three area mechanics and none have been able to
diagnose the problem yet. So far in our troubleshooting we know theres
a link with the cold weather. If its stays in a garage overnight it
seems to start ok in the morning. and there wasn't much problem this
summer. This winter its much worse however. Also, there seems to be
something with the gas cap/tank as well. One mechnic said he found a
faulty code to the gas cap, so we got a new one, but it hasn't helped.
Taking the gas cap off though seems to have some interaction with
starting it anyway. We've tried dry gas, with no change, and had all
the filters possible changed with no improvement.

I am hoping there is some Honda guru who can point me in the right
direction where to take this problem. Before this problem the Odyssey
has had a history with Transmission trouble, and we were never
satisfied with the repairs attempted by the honda dealer(it still
doesn't shift right(hard downshifts) in normal driving, and seems to
bolt in gear from a stop sometimes), and also had the timing belt
replaced which was reccomended given the mileage. Other than that its
been relatively trouble free before the starting problems.

any help is appreciated....