I only put a couple few hundred miles a yr on my Allante. I start it up quite often so I keep the battery connected. When I do drive it, after a few trips or so I will attempt to start it and it does nothing, but seems to have a full battery charge. All the lights on dash etc. work but starter does not turn over . I have at the time played with disconnecting the battery and trying to reset the system but that doesn't seem to do much. But after a while it will start. Is it the starter getting hot and not working and if so how do I trouble shoot that without replacing the starter first.
Also, it seems when the battery does not have a Full charge the lights come on automactically and won't go off. If you turn them off they come back on in a few minutes. What the Heck is that?

Low voltage can do a lot of weird things to an Allante' as far as lights going on and 4 way flashers, etc. When the car does not start, try tilting the steering wheel up and down to all the positions and try to start car at each position. Have you checked for battery drains?

this may also be a good time to look at a GEL battery.
GELs dont spill, dont vent and are CLEAN .. something important
in a car that carries the battery in the passenger compartment.
Red Top Optimas physically fit and have plenty of CCA's for the Allante.
there are others, i just happen to own the Optimas as COSTCO
around the corners carries those.

if you do have a electrical drain, you may also want to consider
a battery tender that keeps the battery charged and/or a
Priority Start automatic battery saver device to disconnect when voltage drops.

after the battery voltage drops below 11.9 volts, the Priority Start
device disconnects the battery to prevent further drain.
when you turn the ignition key on, the battery automatically
re-connects to let the car start.

two solutions for anybody who has a battery drain problem,
or simply stores the cars for the winter.

I tried the ole steering wheel up and down trick, also moving the gear selector back and forth making sure its in park. Also, putting in Neutral and moving the car a few inches then back in park and trying to start hoping it will move something with the flywheel or something. I know I'm reaching, but when you're stranded with a car that won't start you will try anything.
I will have the mechanic check for battery drains next(if it will start).