[Frank7]

Four areas of a cart could cause a shutter at start up.

1-one or more batteries could have a bad cell.

2-Solenoid

3-Controller with bad transistor.

4-Motor brushes.

Typically a 2003 CC is a IQ type of electronic system and the hand held computer that plugs into the system will show a tech a fault.
Your system as described has the older F&R switch and no plug in and must be analyzed by testing components separately.

Hope this helps, call for more.