The mats are safety mats. When you step on them, they should kill power to the machine. If they are folded or wrinkled, they may be triggering the estop, and not allowing the machine to run.
It's likely a safety trip wire switch, usually used to block off an area behind the machine. Trip the wire, and it kills power to the machine.There is also some kind of a pressure switch on top of the electrical cabinet that has a carabiner attached to a leash. If you pull on it with a good bit of force the leash extends and then you can hear a relay in the electrical cabinet click. I have no clue what it does....
Not sure how the pendant works, or what the other stuff does.