Hello Whart,
You can save yourself a trip by doing the following:
Put the key into the ignition, turn the car on (but do not start it) then off, then on, then on, then on again. Leave it in the on position. The check engine light will flash and pause briefly, flash again, then pause longer, then flash and pause briefly.

These flashes will provide the fault code causing the light to come on.

Example:
(Key ON, OFF, ON, OFF, ON)
2 flash, 4 flash, (long pause)
5 flash, 5 flash
Is code "24" your Throttle Position Sensor (TPS)
code "55" means "end of code list"
In this example, your TPS is bad. replace it, unhook the batter for about 5 minutes, and the code will clear.

you can get a full list of codes at:

http://www.allpar.com/fix/codes/index.html

Sorry Luke, Unless whart4 lives in an area with some pretty well established parts stores they won't have a reader for a dodge shadow. They are pre-obd2 cars so the scan tool is a lot different from what we use now.

Stop by a parts store like autozone and they can check it on a computer for free to tell you why the light is on.