OP has it right, but we can add more information. I've been following the discussion over at www.airliners.net where some people know more about this plane's electronics.
First some back story. The SATCOM system is sort of like your cable modem, or more accurately a cell data stick for a laptop. It's a sort of modem that knows how to connect to the satellites. Like a unprovisioned cell phone it still reaches out and says "can I have service", and then gets no answer. ACARS is an application that runs on another computer in the plane. It's sort of like a "twitter feed" for a plane. Short messages can be placed on it and routed off to other places. Boeing offers a service where the plane reports its health back to boeing using this application. Rolls Royce offers a service where the engines report back to them using this service. Pilots can even send short text messages over the service back to their HQ. The GPS system can send a message with its position. ACARS knows how to transmit over HF, VHF, and SATCOM. It also goes through a cleaning house (think twitter again) who routes the individual messages to the right party.
Mayalsia Airlines apparently bought the "limited" package of monitoring. As such ACARS was programmed to send no information to Boeing, and only limited information to Rolls Royce. Compare with the Air France crash in the Atlantic where they subscribed to the "full" suite of monitoring and 29 messages were generated. Further, Mayalsia apparently didn't pay for SATCOM airtime, instead letting it report over HF and VHF. If it was far enough out over water these methods would not be within reach of the radios.
However, the plane still had a SATCOM system on it (comes standard), and it was still like an unprovisioned cell phone saying "can I have service", apparently once per hour. Further the satellites in orbit have directional antennas that cover a particular section of the ground. It appears in this case ACARS was disabled (either intentionally, a small switch in the cockpit) or via failure (fire, or whatever).
The key detail is that while ACARS and many other functions can be turned off from the cockpit, the only circuit breaker for the SATCOM systems are NOT in the cockpit according to experts. It would require going to the electronics room on the plane which is not easy to reach in flight, and more importantly would not be possible to reach if a individual had taken over the plane.
So the stories line up. Boeing received no messages as the plane was not programmed to send them any. Rolls Royce received two during the normal part of flight, and then nothing as the system was turned off or disabled. However that SATCOM modem apparently continued, once per hour, to look for service. I guess the US authorities were able to talk to the satellite provider and get logs of it making those requests, and perhaps even narrowing it down to a specific antenna on the satellite.
On power; the experts say the plane has ~30 minutes of battery in the case of total electrical failure. In flight it also has a ram air turbine (think mini-windmill) that can generate enough power. If it did a "miracle on the hudson" style landing in water and it somehow stayed afloat (being under water even 1' makes the sat signal too week) batteries would only last ~30 minutes.
One of the most bizarre incidents ever recorded. The outcome of this is going to be very interesting.