In the decompression scenario, though, the aircraft's transponder would have remained working. This would have allowed the aircraft to be tracked accurately and the authorities would have known about the problem before it even crashed. In the past, military jets have been scrambled to intercept airliners that have gone off course (the Helios one being a case in point). I would certainly expect that to happen in the light of 9-11, and if it crossed any borders it shouldn't have.
Once the transponder stopped working, tracking the aircraft would have to rely on primary radar, i.e. a return bounced off the aircraft's hull itself, rather than a packet of data interrogated from the aircraft containing accurate identification and position information. Yes, you'd expect a country to be looking for that sort of thing in its' airspace, but it's a lot more difficult to tie to an individual aircraft, radar range would be much reduced and, if the aircraft was over international waters by then, maybe they didn't care much. You only have to look at the flight's trace on flightradar24.com, etc. to see that it went missing in an area with very good secondary radar coverage, yet no wreckage has been found there.
What would you do if you were going to divert a jet from its' course and you didn't want to be tracked? Wait until you're established en-route over the sea, turn off the transponder, descend to low level out of primary radar coverage, then toddle off to where you want to be, perhaps? Maybe, that's what happened, but the aircraft ditched from low level and thus didn't spread much wreckage and wasn't where it "should" have been, hence very hard to locate?
There's the possibility that the aircraft was carrying satellite based comms equipment, which is often used to update ground stations on the aircraft's status in real-time. It's odd that nothing has been mentioned about that, although I did hear a report that Rolls Royce were still receiving monitoring data from the engine systems via such a link after the aircraft lost contact. It seems inconceivable that such a data link wouldn't also include GPS position.
As for mobile phones - well, an airliner is a pretty effective Faraday cage, so, for a mobile phone to get a signal out through the fuselage is going some. To then make it hundreds of miles to a base station on the ground is impossible. Mobile phones are designed to work within 10-20 of miles of a base site at the most. Besides, digital mobile phone networks have other constraints that mean there are absolute limits on how far a mobile can be from the base site, and how fast it can be travelling, due to round trip delay and doppler issues, so no, I don't think mobile phones on board will have come into play, except that, if the aircraft landed anywhere near civilisation, they would almost certainly have given the game away.