Why can’t I power up the drone system

The Anti-Ship Drone is armed with a laser, which does damage to a single room targeted randomly by the drone. It also takes the shields down one level if it hits a shield..

The Anti-Ship Beam Drone is armed with a beam weapon, which does damage to multiple rooms along the path of the beam, but which does not affect shields at all. Instead, shields affect the beam, in that each level of shield reduces the damage of the beam. Since the Anti-Ship Beam Drone only does 1 damage per room, even a single active shield can render the Anti-Ship Beam Drone completely useless.

Breach bombs damage systems and crew, and cause cracks, but don't hurt hulls. Alternate bombing the medical bay and the O₂ generator. Put priority on whichever one the crew is trying to repair. Eventually they'll have so little health they won't try to repair things, and you can just wait. If the ship doesn't have a medical bay it's even easier - just bomb the O₂ generator until they stop trying to repair it.

If you're taking this tack, it helps to upgrade your own shields (and maybe have a defense drone) so you can sit and wait them out without having to waste missiles bombing their weapons as well.

Ion weapons can help, but it's hard to get enough of them to punch through 3-4 shields reliably, while you are still getting shot at. If you have them, great, but don't prioritize them.

You are correct about sensors. Don't even bother trying to kill crew without damaging the ship until you have the first sensor upgrade or a slug crew member.