My Esteem does not change gears when driving.

Thanks for the recommendation but I have already checked the fluid level and it's OK.

Then it looks like it is your shift solenoid valves. They talk to the transmission control module. An ODBII scantool will probably not be able to tell you codes from the TCM. You might get lucky and check the following fuses: Fuse 8 in the relay box, Fuse 21 & 23 in the Fuse Junction Block.