No, there shouldn't be any fluid in the computer.
Dot 3
ATF+4
You can add transmission fluid to your 2003 Chrysler through the transmission fluid dipstick holder. It is best to use a funnel to prevent spilling the transmission fluid.
Mopar ATF+4
Automatic holds almost nine quarts.
Low fluid, plugged filter, internal failure.
It's a small silver reservoir with black top, sitting near the passanger side end of the engine. It should be filled ONLY with Chrysler approved +4 transmission fluid.
Total capacity is almost nine quarts.
ATF+4ATF+4
Flushing involves a machine that hooks up to the cooler lines and pushes fluid in as the transmission pumps it out.
If the transmission computer detects a malfunction it defaults to second gear. It will have codes stored. Other causes include low fluid,and internal failure.
It is on the driver side under the hood, near the base of the windshield.