93Bonne SE Hard Cold Start Stuck in 1st gear

[DaveG]

Have a 93 Bonnevill SE 3800. Car exhibits problem when it is colder <
25 deg F. It is hard to start, must crank a long time, it likes to "catch"
or start when the throttle is about 3/4 of the way depressed. Once I feel
it kick at the throttle position it will for sure start once I keep it at this position. Once starts it has good power, but will idle like around 2 to 3K
rpm. Service Engine Soon light is on. Upon drving power is good, but is
STUCK in waht feels like 1st gear. Can get up to about 35 MPH with RPM like 4K and beyond that it feels that the transmission is not even "connected" like the engine is just free spinning. Once car slows
you can then feel the acceleration of the car from the engine. Best
description, if I drive it maybe a mile and warm it more the car shifting
will work normally but ONLY after shutting off car for maybe 5 seconds and restarting which again requires much cranking and the engine
will kick on at certain throttle position(3/4 depressed is the sweet spot).
At most tempaeratures of late<45F it is hard start, the 1st gear stuck
condition seems to occur mostly below 25deg. F. To summariz the hard start is always occuring, the stuck in first gear is occuring more often
now with the cold weather here in Michigan.

Any thoughts? Was going to take to Autozone for codes, but grasping that someone may have falling into this same problem. This is a very good car, well engineered, with 113K miles on it. Suspecting it is plagued
by maybe a less than $100 part?