F150 starting issue

OK so, I have seen a couple threads on here that
relate to my problem and I used the diagnostic
steps for a couple of items.

Issue:
When my step son turns the ignition, it makes one
loud click that seems to come from the starter but
it won't turn over.

He had this issue one other time when I was out of
town and we transferred money so he could buy a
new battery (his grandfather told him that was the
issue)
This solved the problem for the last 4 days but now
the same problem is back (he said this is what
happened last time).

So I read up on this forum to trace the starting
sequence and possible problems along the line.
I jumped the solenoid (easiest test first) and
makes same single click at the starter. So ruled
out.
Pulled the plug on the DTR and totally nothing.  
Plugged back in and same single loud click at the
starter. So ruled out for now.
Removed the starter at took to part store to test,
test showed it was "sluggish" so I bought a new
one and kept the old to rule out starter.  Installed
new one.....same friggin problem! One single loud
click at the starter.
Engine turns (cranked by hand with a wrench) so
the engine is not seized.

Totally and completely lost now.
Any suggestions would be appreciated.