We NEED HELP

My boyfriend owns a 94 dodge
dakota. Bought fairly cheap, used.
He hasnt had it long and it had slight
issues backfiring sense the purchase.
It idols fine usually but recently at
stops it lags and sometimes does die
in the intersection upon take off. So
the backfiring and dying has
increased but now new issues like the
headlights go dim and sometimes
completely gone but the truck is still
running by the time the headlights are
completely out but shortly after it
loses all juice. We've had the battery
checked at auto zone and they said
the battery was bad. But then my
boyfriends dad checked the battery
the same day, different tool and it
read as fine. Also the wipers sropped
suddenly while driving too and there
is an extra wire attached to the
battery cable but we havent had tome
to follow it to its connection.
We are at a loss for solutions. And
money is tight right now or we wpuld
put it in a shop.
Please help us.