Same starter both turbo and non turbo.
A problem I have found with these is the solenoid connection.
My dad's neighbour has just had this identical problem, slow turning etc, even with new battery and new alternator, both of which were not needed.
In his case someone had crimped a connector onto the solenoid feed wire, presumably due to being damaged or whatever, tracked it down to this having too high a resistance, the solenoid are VERY voltage sensitive, and if not enough there they don't hold firm against the contacts inside the solenoid when bridging the power terminals.
Anyway, cut off soldered on a connector, the engine nearly turned the car over, not literally but compared with before!!
That was 2 months ago and hasn't missed a beat since, this one had also been to 3 garages, and a auto sparky who said battery and alt, it's now running perfectly on the old stuff and he got his money back for the stuff that was fitted he didn't need.
tabetha