Test the operation of the lens mechanism as follows.

Gently lift the ribbon cable connections off the two tags on the back of the motor.

Apply power to the motor from a 3v battery pack by connecting it to the two tags on the motor. Apply positive to the terminal to the front of the lens to extend it, or to the back of the lens to retract. (Keep all ribbons out of the way - applying power inadvertently to the wrong place could damage something.)

Disassembly of the lens is covered in the companion guide "Canon PowerShot SX200 IS Lens Disassembly". This should allow most cases of stuck lenses and the dreaded "Lens Error" to be diagnosed, and hopefully fixed.