The form of investigation may well depend on what is found at the bottom of the Indian Ocean, and what can be recovered. It has been reported that the Malaysian government has already started its own investigation into the performance of the civil aviation and military authorities.
... I read that the crucial 'black box' is unlikely to contain the data about the critical moment when the aircraft departed from its normal route since the 'tape' would have 'looped' since then, i.e. does not hold details of an entire potential flight endurance. All the hijacker had to do was to keep the plane going long enough and bingo, no evidence!
You have to beware of journalists being sloppy with the terminology, as there are actually two data recorders. The Cockpit Voice Recorder (CVR) is the one that operates on a two-hour overwriting loop, and depending on what had happened, may indeed be of limited use. The one that lay people tend to think of as the "black box" is the Flight Data Recorder (FDR), which can record hundreds of parameters from the aircraft systems for up to 25 hours.
Not having a record of any conversation in the cockpit at the point when MH370 went off-course will be problematic, but there is a hell of a lot that the investigators can glean from analysing the FDR, such as autopilot engagement, altitude, control inputs et cetera, which will go some way to determining if the plane was actually being actively flown between going dark over the Gulf of Thailand and the point over the Andaman Sea or Indian Ocean where it finally turned south.