Hey Reverhart, I was reading on another forum on an issue that you thought you had with your transmission back in 1997. I believe your H1 was surging up pretty heavy (making your vehicle continue forward) when you drove slow in overdrive as well as other gears.
I have a 2002 H1 all stock with the exception of a PMD relocator from Predator Performance that I replaced at 19,000 miles due to malfunction. My H1 started with these surging issues a month ago. First time it did it while warming up( I have a remote start and fire it up to cool the cab with the A/C).Since it surged & went down to normal idle all byitself I got in the vehicle and didnt think much of it until I drove off realizing my vehicle was in a weird limp mode.
I had heard of H1's going into limp mode when the speed sensors are dirty so I drove back home cleaned them off & turned it back on thus solving the issue for about a week. Soon after that my vehicle started surging more often, once even stoping on me like when the PMD starts failing. A quick call back to Predator Performance and Josh informed me that he has had some PMD's fail the same way and that I should replace mine once again.
A day before my new PMD arrived the H1 surged at a red light for like 30 seconds while I was behind standing traffic. I screwed up & didnt throw it in neutral keeping the H1 from lunging forward with only my brakes because it had never surged for so long and the police officer in front of me thought that I was reving my H1 behind him.
Finally light turns green H1 idling normal and I drive home with no more issues. I get in my H1 one some time later only to find out that my Reverse is acting like neutral, my neutral is like drive and park seems to be wanting to go into gear when i go into park but manages to stay in park. I plugged the H1 into my friends scanner and picked up codes that seemed to correlate with Josh's predictions about the PMD. That solved the surging but my new tranny problem continues. The scanner also doesnt show the tranny shifting as i go through the gears and it looks as if Selenoid 1 doesnt ever disengage.

Any info as to what you learned from your issues would be greatly appreciated. If anybody else has had similar problems I would appreciate any help. I dont want to replace a whole tranny that might not have to be replaced because my hummer only has 40,000 miles

your issue sounds a little different than mine
mine would surge in gears (f and R) but if I shifted it to N it would idle fine, aslos when I accelerated past 5-10 mph the surge would go awa-- it was basaiclly at idle
I swapped transmissions and still has the same issue-- (Was pissed)
I had already changed the pmd to my spare--

when I was dismantling the truck to do a duramx conversion I went to unplug the harness from the computer and found it melted to the pcm, a couple of pins had melted together-- when I looked at what the pins controled--can you guess--the tranmission
might want to check your cable going to the transmission, and the computer plugs?

btw if you inspect your harness going to the tranny and find an issue let me know I bought a new one and never used it it was very epensive

I will check and get back to you, thanks.

Found the problem, Planetary gears are fucked. I thought the 4l80E transmission was supposed to be tough. 40,000 miles and time for another one isnt fun at all.

bummer