Having worked rebuilding starters and alternators for a summer..

My VW bug did a similar thing one time, turned out to be a broken wire on the solenoid..
but one has to be careful, turns out the start actaully had a shorted field...
A brand new car battery 800+amps couldn't even turn the thing over unless all was perfect..
its worth, for his situation (probably not the means or tools to pull it apart) to just get a reman or something..
Perhaps a bad field, stuck brushes, anything...hard to say..

Thought the dim lights would seem to indicate overdraw of power=shorted field/communtator...