Why doesn't my pressure tank fill as expected?
6 PSI amounts to 15 or 16 vertical feet rise, at most. 200 feet sideways and 15 feet up, not 200 feet up.

As such, I'd have to say your pump appears to be in need of service or replacement, based on what can be gleaned from what you've written. No water is going into the tank because the pump is evidently unable to make 30 lbs of pressure, much less 50. 6 PSI is not a functional well pump.

You described this as a shallow well pump - is it in fact a jet pump (recirculating, 2 pipes to the well), or is it in fact a straight shallow well pump (pure suction, one pipe to the well, less than 27 feet to the water surface)? A jet pump introduces a few more things that could be screwed up.

If you are facing replacement and it's a jet pump, I'd strongly suggest moving to  submersible, as they are much more efficient than jets, (you could replace a 1 hp jet with a 1/2 or 3/4 submersible and pump more water in most cases) and with today's technology, also more reliable.