Dave, if the dash mounted push button starter switch is just causing the starter motor to try to turn the engine over, then it is not the problem.  This switch sends a signal to the starter solenoid.  The solenoid  pulls the starter gears into the flywheel and it at the same time, closes a contact to apply 12vdc to the starter motor. 

The fastest and easiest way to eliminate concerns about wiring is to hook up some jumper cables from the installed battery to a good ground point and also the + terminal directly to the starter motor.  Then try and start.  If everything’s ok and it starts, you have a #2 gauge wiring or connection/terminal problem. 

If it doesn’t change anything and still won’t turn over, then you may have either a battery problem or a starter motor problem.  I replaced my starter motor and solenoid last year.  Rebuilt Bosch from one of the discount auto stores.  

Starter and solenoid were <$50. 

New batteries can be bad.  Have it tested.  It is free at most of the discount auto stores. 

Sometimes in Western New York we have 90 degrees humid weather and I have had the same problem car turned over slow when engine was hot . Tried lots of things . Cables, posts , Battery relay ,etc . One day I took my new battery to Auto Zone . My 6 month old battery was shot ! Replaced no problems since .. Something I thought about . Could I put a battery in with a higher could cranking power or would that be a mistake .

Samba VW site has forum with some listings for hard to start when hot. The site is a good place to look for info on VW based engines.