I have a 2008 Chrysler Aspen, seems like bad transmission, or something else, how can I be sure of the diagnosis. When I mash down on the accelerator pedal, the rpms goes up high before it moves.

SOURCE: Transmission problem

If the S light is blinking, this indicates that there is an electrical problem somewhere it the TCM circuit. I have included a link that takes you to an excellent page which shows you how to read the codes and what they mean.
http://home.earthlink.net/~michaelpkeefe/HowTo_Codes.htm
Also, The top solenoids are for the lockup clutch and the bottom ones are the shift solenoids.
As for the Immobilizer causing problems, if it was incorrectly wired to the TCM, then it could possibly cause a problem.

SOURCE: 1996 Explorer Transmission slipping badly A4LD

check transmission fluid.if look or smell burnt change fluid and filter.

SOURCE: Transmission problems

Could be a couple different issues, First trans is slipping, which means time to repair. The other is the fluid needs to be changed. The best thing to do is have it checked out, they might be able to fix easy, if you wait you will do more damage then the cost will be much higher.

SOURCE: I had transmission rebuilt on 2002 Saturn sl1

If the rpm's are high and not shifting properly take it back to were you had it rebuilt, anyone who is good should honor their work.

SOURCE: rendezvous 04, the rpms stay idling high without pressing gas.

BUICK RENDEZVOUS IDLES UP REALLY HIGH...WITHOUT PRESSING GAS. WHAT IS THIS?