How can I determine if the car is in limp mode? Would a computer diagnostic reveal this? Or is there another way to find out?

Limp Mode = stuck in 4th gear. Accelerate and see if your car shifts or not.

does your cluster not work? it should tell you in the check control display.

but I guess this is not always accurate. ???

CEL was on originally when the problem started, but then it went out, and problem is still happening. Could it be in limp mode w/o any warnings?

Does it upshift when you try to drive it or not?