Once you link an activation module to a working systems computer with at least one module linked, that computer no longer shows up on the weapons menu (hotkey "G) even after you unlink the activation module from the computer. Tested on cannon and inhibitor computers, local and online, multiple entities. You can break all the computers on a ship with one activation module.
Re-logging does not correct. The ship permanently believe the computer should not be directly accessible through the menu/hotbar.
Only deleting and re-placing the computer then re-linking it to its modules corrects this.