G'day mate!
I think your triple is experiencing the exact same symptoms mine did -- bad sprag clutch. The sprag clutch is incorporated as a safety mechanism insuring torque can only be applied from the electric motor to the engine and not vice versa (e.g. when the engine is actually running). Unfortunately the pre-07 models seem to be made of tinsel.
See my thread:
http://www.triumphrat.net/speed-trip...n-t-start.html
On the upside, you are in luck as most triumph dealers, at least on our side of the pacific, will replace the sprag clutch as a good-will gesture to 07+ spec. Also if you've been experiencing long cranking issues (2+ turns) prior to this, the update seems to fix that too.