H122,
Another possibility could be the starter gen, if it has badly worn brushes, or a duff commutator. Allison specifically require the throttle to be opened between 12-15% Ng, I have never subscribed to the technique of letting the Ng peak. Too much chance of no ergs left in the battery to properly spark the ignitors and give a clean start. I had Nicads in some 206's I operated, and haven't found much difference with lead acids, except a run of Sonneshein (sp?) units when they couldn't crank as advertised. Switched to Hawker batteries last year, and no further problems.
One 206 I fly has the fastest spin up of a C20 I've ever encountered, crack the throttle at 12% and it's past 15% before the fuel lights off! All other parameters are normal, it's been the same for years, even after a mini.
I'd be looking at the battery contactor in the nose, reckon Steve had the right idea there.