There was a rumor circulating that the manufacturer of the engines (Rolls Royce) had satellite based telemetry on the engines to assist with maintenance planning.
I have refrained from commenting here because I'm not sure if I am permitted by job. I won't get into specifics but what Mark R says here is correct.
I also don't know the specifics of a foreign country's ATC system but if its similar to the US then here is the problem. My guess is that the area in which the flight was traveling was non radar. There are no physical radar sites located in the ocean. The usual requirements are for the pilots to report the aircraft's position every hour.
It could be that the last position they have on the aircraft is the pilot report. Having the transponder on/off doesn't really matter in a non radar environment (for ATC) but it does provide the pilots with TCAS alerts so that is why they remain on. Going back a couple posts, pilots were required to turn off their transponders after they land - however, with upgraded ATC equipment they leave them on so ground controllers can positively identify them on ASDE-X.
http://www.youtube.com/watch?v=O2dg1750aXk
If the aircraft was not SATCOM equipped then there is no way to send messages. ACARS messages are sent over VORs and without one in the ocean it would be impossible. If the plane was flying in non radar airspace the only way they could be identified is when they got back into radar range or the pilots reported their position. Its possible they could have flown until they ran out of gas.
Turning off a transponder doesn't make an aircraft invisible to ATC*. It would still show up on radar as a target but it would not have any information related to it i.e.. call sign, speed. I have seen birds appear on my radar scope. If you "click" on the target it will give an altitude but nothing else.
Most people don't realize that the entire North Atlantic is non radar airspace. Until recently pilots had to verbally give their position reports to a radio operator. The RO would take down the coordinates and relay those to the ATC that was responsible for the flight. Now, a lot of planes are equipped with ADS (satellite) and those reports are transmitted by the plane's flight management computer.
Recently, there was a plane en-route from Johannesburg south africa to Atlanta, GA. It was ADS equipped and was transitioning from one ATC to another. The pilots have to "dial" in the next ATC address into their computer and accidentally logged onto the incorrect one (Alaska). The flight crew never checked on and flew for 4 hours in the non radar airspace. Long story short, it was only when it appeared on radar that ATC realized they were there....and head on with other aircraft. The flight crew were issued pilot deviations.
This post is really long and most people probably won't read it all so I'll wrap it up. The strange thing is that the route they were flying seems to be traveled pretty heavily. If the plane went down then the ELTs should be going off and they should be getting picked up. The waters in that region are not very deep so the crash site should be easy identified. My guess is that if they haven't been found by now they are probably looking in the wrong places.