A B767-200's autothrottle system failed and would not engage on takeoff. As a result the FMC position did not update before liftoff and a slight track deviation resulted as the VOR updated the FMC. The aircraft is not GPS equipped.

Narrative

ATC clearance was the RNAV departure Runway XX RNAV. Before taking the runway we noticed the aircraft was not exactly center line on Runway XX. During the takeoff roll N1 was selected however the auto throttles did not engage. The Captain manually set takeoff thrust and the takeoff was normal. At 400' when LNAV was selected the Flight Director commanded a slight turn to the right then after a moment a turn back to the left. It was at this time ATC asked if we were flying direct to the first fix. The Captain responded yes and checked the cross track error which indicated .2NM west of course. It wasn't until a couple of minutes later that we realized the turns were the due to the improper alignment of the FMC. We believe the reason the Flight Director commanded the turn was due to inoperative auto throttles and no runway update before takeoff. It appeared to ATC radar that we might have been flying a different departure which includes a westerly turn shortly after takeoff. There was no conflict with another aircraft nor was airspace compromised. However with a larger position deviation and inoperative auto throttles; selecting LNAV at 400' could be a problem. The auto throttles were written up and placed on MEL. A fix could include a procedure to return to manual runway updates before takeoff in the event N1 update malfunctions on takeoff. Or; vectors should be requested of ATC since a last minute abnormality makes it impossible to fly an accurate RNAV departure.