I suspect the transmission is locked up between two gears thus the starter can not crank the engine. I suggest you unlock the transmission first then try the starter . If it has been physically unable to turn due to the tranny lock and multiple tries at starting it's possible it has been damaged. If it does not engage and turn after freeing the tranny then remove it and have it checked. That being said it does not explain no power to the other electrical components. As mentioned above the wire to the ammeter needs to be checked and also the ammeter itself. Also when checking for continuity the test meter should be grounded to the engine not the battery . 

@dennis-christianson  The small wire that feeds the dash from the starting switch post has nothing to do with the cranking of the engine.

@steve-d If John is attempting to crank the engine with the clutch pedal down, it would eliminate the problem you describe, for purposes of starting the engine.

Mike

I was talking about the gauges and lights, guess I didn’t make that clear.

Dennis and Mike I agree with both of you . It seems however whenever a suggestion is made new information is added. It is hard to diagnose a problem without all the known facts. Still after all post I am not certain if the starter attempts to engage or if it is completely non operable. Also as Dennis pointed out all power flows thru the wire to the ammeter and then the ammeter however using the neg post on the battery for ground eliminates the testing of the engine ground circuit. Why was the battery replaced and simply not recharged? Is the starter non functional due to multiple attempts  to try to start? At this point I am guessing that even the new battery needs charging . 

I am unable to get the starter to crank over, I get nothing. Do you think the starter switch might be bad?  How can I check the switch? Can I bypass the switch to check the starter?

@buckaroo01-2-2-2-2 "I would check the switch next. Disconnect the battery ground and then remove the positive cable from the starter. Take the two screws out and look it over. The switch contacts and the copper lug on the starter should be bright. Post a picture if you can. New switches are available and the lugs can be cleaned if not too burnt." as previously posted with photos by Dave Dunton . Please go back and read all post and then follow up on the suggestions that you have not responded to. Until you do that I do not think you will solve the issue. 

I

Posted by: @buckaroo01-2-2-2-2

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 Can I bypass the switch to check the starter?

You can remove the switch by removing the two screws. If you then touch the battery cable to the copper lug momentarily it'll tell you if the starter is working. Make sure the car is in neutral and just hold the positive cable against the lug for a moment. If the switch lug is fried, you can often turn it around inside the switch & use the fresh end rather than buying a new switch.

A couple other thoughts here. If the car still has the vacuum shift, it is very hard (nearly impossible) to move the shift lever without the engine running which could be why John thinks it’s locked in gear. As Mike mentioned, pushing the clutch in eliminates this issue. Next, I would recommend John gets the engine to crank first, without worrying about power to the key switch, gauges etc.  Once the engine cranks, the other issues may resolve themselves. I would remove the new battery to provide better access to the positive battery cable connection at the starter and the battery ground point to the engine. Even though a test meter shows voltage, a loose or dirty connection will not pass the required amperage to crank the engine. Cleaning and tightening these connections has been recommended several times before but worth again verifying, especially if the ground strap is connected to the frame. Make sure the ground strap is the proper size (factory was braided) and verify it’s secured to the tapped hole on the bell housing rather than the frame. If it is connected to the frame, a second ground strap from the frame to the engine is highly recommended. It may have been asked before but would be great if John could post pictures.