The right hand drop down target solenoid remains energized forcing the targets up.
With power off the solenoid it operates freely, but as soon as power is applied the solenoid is energized.
Has anyone had a simular problem?
Most likely the transistor for that solenoid has gone.
Do you have a multimeter and handy with a soldering iron?
Appears to be solenoid # 15...I'm trying to find a set of schematics so we can point you in the right direction..
http://www.pinrepair.com/bally/index3.htm#driver