Over a period of only two weeks, the results would be horrendous. As we know - any major slowdown of the rotation - means that this energy (rotational kinetic energy) has to go somewhere! Assuming total stoppage in a mere 2 weeks, most of the rotational kinetic energy (defined by the equation KE(R) = Iw^2/2 where I is the moment of inertia of the Earth as a sphere (0.4 MR^2 where M is the mass, R the radius) , and w is the angular velocity) would go into translational kinetic energy and heat.
This means that temperatures in the crust would rise dramatically, no doubt triggering many major earthquakes, volcanoes and sea floor instability. In all the regions where tectonic plates are in contact or a lot of pressure exists, conditions would be uninhabitable - intolerable.
Even worse, as the motion of the Earth's core comes to a halt, the dynamo process - that gives rise to its magnetic field and its magnetosphere- would also halt. (By "dynamo" I mean that the moving large scale electric currents in the molten core, give rise to a magnetic field for the whole planet.)
As we know, high energy solar particles are currently "filtered" along the Earth's magnetic field lines near its magnetic north and south poles. With rotation halted, and core motion gone, that magnetic field vanishes. It is no more.
This means that all the powerful solar radiation and high energy particles will now come directly into the Earth, saturating power grids, and probably incapacitating whole countries. It would be especially bad during severe solar storms and major solar flares.
Since so many natural processes depend on Earth's magnetic field (there is some evidence that even honeybees use it in finding directions), it is clear that much of life on Earth - certainly as we know it- would be threatened unless major technological solutions could be implemented in a very short time.
For a 2-year slowdown progression, the effects would be noiceably less severe- but still destabilizing. There'd still be enhanced crustal temperatures - probably much higher frequency of earthquakes, volcanoes - maybe even tsunamis. The latter could well be exacerbated with much higher tides than normal around the world (due to the braking effects). You'd certainly get a lot more "rogue waves" - such as the one recently reported in the media - a 70-footer- that crashed into a passenger cruise ship around S. Carolina.
Ultimately, at the end of the interval, with all rotation ceasing - the same effects noted above to do with the disappearance of Earth's magnetic field would come into play.
Supplement from 12/22/2008 06:52pm:
All of this can be projected or expected based on the physics we know. In particular, how energy must transfer from one form to another, and how it must affect already relatively unstable regions of the Earth (say with pressure from tectonic plates) - and how inter-dependent delicate natural processes must be affected if, for example, the Earth's magnetic field suddenly stopped.
Of course, as a footnote, all this is by way of sheer speculation - in answering your hypothetical question. The actual chance of the Earth doing any such thing is slim, and none.
Supplement from 12/23/2008 12:20am:
After the Earth's EM field collapses, within a few months, we'd be back in the Stone Age; a full year and everything is 'Nuked'
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