How do I prevent video interference caused by electric motors

Yea but that doesn't explain why the normal batteries have the same problem. I understand the use of the Main capacitor, to get rid of any voltage spikes or dips. But if the power supply doesn't have enough current to supply to everything as it is, then the capacitor won't have enough charge to do its job.

Yeah, if the power supply can't supply enough current, that's certainly needs to be fixed.
I thought OP was using a huge old PC supply.

Also, the business with the Main Capacitor is an illustrative point. It works best IF your
controller is competently designed, and then helps deal with the battery leads, which may
be longish for any #of reasons. OTOH, if everything in the ckt has long leads with nontrivial
inductance, then the cap probably won't do much.

Good design is a systems-level solution. Would be interesting to know how auto manufacturers
deal specifically with the brownout problem when the starter motor cranks. I imagine there's
a lot of brownout protection cktry inside the computer box.