I have replaced the starter, the battery, and checked the battery ground and the transmission to frame ground. When starting there is nothing but a "click".
If I keep trying it will eventually, all of a sudden, turn over and start. What the heck? Where do I start and how?
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I'd clean battery terminals at battery and starter - coating with dielectric grease. Same with grounds (to include where it contacts chassis). Then try shorting the terminals on the starter. If it turns over then it's the ignition switch which isn't very expensive (I see you have stock VW one).
Starter relay?
Did your replacement starter come with its own solenoid or did you have to transfer your old one????? If you had to transfer the old one, I would bet the contacts within the solenoid are "toast".....
This is a typical VW starter problem. The voltage runs from the battery to the terminal on the starter motor, back to the switch and then back again to the solenoid. Front to back to front to back, voltage drop in all of the cables and if there is any corrosion on connection points there wont be enough voltage to pull in the solenoid. Couple things you can do;
1) Clean, clean, clean, any connection point to limit voltage drops and replace any corroded wire.
2) Add an external solenoid wired from the battery right to the starter solenoid to get direct battery voltage to the starter solenoid. A lot of VW places sell these as "hard start" kits.
Hope this helps.
Chris
Remember in donor VW the batter was within a foot or two of the starter under rear seat ---- not way up front 10' away like we do in the Speedsters. Its recommended to use very heavy gauge battery cable wire between battery and starter.
I replaced the starter including the solenoid. I'm pretty sure that it is not the new starter & solenoid as the old starter was doing the same thing, that is why I replace the starter with the new one.
How do I test the ignition switch?
Is it hard to replace and are there instruction online to do so, if needed?
My Speedster is based off a 1973 beetle.
Lots of these cars have the inexpensive EMPI battery isolation switch behind the passenger's seat. They've been known to fail.
Lots of these cars have the inexpensive EMPI battery isolation switch behind the passenger's seat. They've been known to fail.
An EMPI part failing.....very surprising. 
Exactly.
I'm good then - mine came from Harbor Freight!
My only two cents are these:
1. Check and clean the connections of the ground strap from the frame/pan to the transaxle, as well as the ground connection from the battery to the frame/pan.
2. Install a "switch saver" relay close to the starter (within a foot or so) driven by the "start" tab of the starter switch (the same wire that now goes to the starter solenoid). When the key is turned to "start" that relay should be energized, that's all. Provide a robust 12V feed to the relay's switched contacts ( like a 14 ga wire), and an equally robust wire from the relay's switched contact to the solenoid's starter tab (which used to connect to the key switch). This should eliminate any resistance from the key switch and/or the wires going fore and aft And provide the best 12V possible to the starter solenoid to make it engage the starter.
This is an old automotive electrician procedure. Always put an "external star washer" UNDER the terminal before you put the nut on. Two things happen.....the "star washer' keeps the terminal from spinning when you tighten the nut and digs in to the surface under it and over it to make a permanent and excellent contact in both directions and keeps everything from loosening. If you don't believe me just check out any "original" factory connection from most Manufacturers. I have followed this procedure for more than 50 years and never have had a problem with a bad connection.......Bruce
Bruce, good advice. 
MUCH THANKS !!!!
After much testing and searching, I have found it to be the negative cable from the battery. Cut off 6 inches of "old not so shinny copper" and striped back to give new shinny cooper and perfection. Amazing how this cable deteriorated
Again Thanks
So I was right. It was too much resistance in the battery cables.
And Bruce, you are so right. I've been using star washers for years. We used them back when I installed car radios and cellphones. No returns......so they work. I'd scrape the paint too.
