Something similar happened years ago to a mate’s car.
All the electrics worked OK, but it wouldn’t turn over. He called out the AA/RAC & the guy removed the battery leads from the battery, cleaned up the battery posts & inside of the lead clamps with a bit of sandpaper, reconnected them & it started first time.
Seems that whilst the battery connection was good enough to provide power for lights etc. there was enough corrosion &/or the clamps weren’t quite tight enough to allow the amount of flow needed to start it.
Probably not this, but it’s a free & easy enough check to rule it out.
definitely no click.
the button is a sealed unit (not like a road bike where you can “clean out” underneath)
It doesn’t seem to have a side stand switch and I am sure the kill switch is ok.
I think I have tested all connections, but have some help with this tomorrow as next step.
how difficult is replacing a starter motor?
Two completely different faults you mention. A faulty start button would cause a ‘no crank no start’ issue and this appears to have been the problem vs a blocked carburettor would cause a ‘crank no start’ issue.