There's a lot of talk about magnetos on this thread, but the OP says the problem is not that it doesn't start, but rather that it doesn't turn over, or at least is very reluctant to do so, therefore I can't see what relevance the magnetos have.
If the battery is in good condition and fully charged, (I know it's new, but that doesn't necessarily mean it is in good condition or fully charged!) then I would check the thick wiring between the battery and the starter, including the -ve/ground connection. However most probably it is an issue with the starter motor, such as worn or poorly contacting brushes.