I have a 1992 Pontiac Grand Prix, 2 door, 3.1 litre engine, overdrive.
We bought it used with 150k miles for $1000 from a dealer. One problem
that started when we got it and has been much worse during the cold
months is a tendency for the car to need to heat up for a long time
before it will drive away. It will START fine, but the transmission
won't "engage." You put it in reverse or drive, regardless, it refuses
to budge (besides rolling).

For some reason, revving the engine speeds up the process. It will rev
up to 4k on the tachometer, then it won't rev further, as if there's a
lock or something (it redlines around 6k if I recall). But regardless,
at times in fact, it will stubbornly refuse to "engage" in gear at all
unless you rev it, unless you've let it run for 5-10 minutes; in one
extreme case, it took 30 (yes, thirty) minutes for it to engage.

There is no slippage or other typical transmission problems, just the
delay in engaging at startup. Once it engages, it takes off fine and
strong, and downshifts and upshits with no delays or slippage or any
such thing.

The fluid (not the filter) has been changed, no difference. For some
reason, when my wife changed the tranmissions fluid, she didn't tell
them to change the filter and they didn't. (Argh!)

Has anyone of this problem before? Is a known issue with Grand Prixs or
something? One person said that the transmission fluid is cold in the
morning and needs time to warm up, but I've never seen a car has this
behavior in any type of weather. Is it indicative of a looming major
transmission problem? Tips in general?