Another (relatively) short one: Communications, sensors and certain hullmods which add functionality (Eg. Dedicated targeting core) would be subject to malfunctions and disability in the same way as engines and weapons.
If communications are disabled, no orders can be given to that ship until they're back online - furthermore, any ship that can only be "seen" by one with disabled comms would not be shared with the rest of the team (ie player). If the player's ship's comms are disabled, it would prevent giving orders to any other ship.
When sensors are disabled, the afflicted ship is unable to target enemy ships, nor can it reveal enemies on the command map, ie use its sensors.
Shields is an iffy one, potentially messing with game balance a bit too much. It'd probably have to have an extremely low chance of being disabled, or repaired relatively quick.
Ship systems (ie phase skimmer/cloak, accelerated ammo feeder etc) is equally iffy, and would probably require delicate balancing for each.
As for hull mods, it's hard to list which ones would really fit with this. DTC/ITU, Advanced Optics, ECCM are the only ones I think would be logical.
All this would go towards making EMP weapons much more dangerous, mind, as well as combat in general and low CR.