2001 Dodge Omni won't start

The click is your starter solenoid. The inability of the motor to turn the engine over could be insufficient battery power or a jammed starter motor.
The first thing to check is that the reconnected Battery terminals are making a good connection to the battery and that the battery actually has Juice. (Try a jump start)
You should also try gently tapping your starter motor with a hammer a couple of times and then trying to start the car again. The motor can seize up and the tapping can free it up. Don't tap too hard though. If you crack any of the magnets lining the motor stator. It will likely jam up permanently.