electrical problems... starter engages when cables are put on battery
Check ignition switch starter wire at the starter
There are few things to check why your starter engages.
Have you recently installed a new stater?
Overtightening might damage the starter.
It might be also that your starter soleniod is already bad.
Check the starter relay , parts inside might be rusted or stucked up. Try to listen if it stil clicks every time you hit the ignition switch .
A poor ground in the starter might be one as well. Try to check the terminals if they are still in good shape.
The points on the starter could also be bad, or something might have shorted them in a way. Check those as well.