I was told on this Dakota that the check valve (I don't know if that's
> actually what it's called) is located in the tank with the fuel pump.
Correct.
> I guess my question is this: If I replace the fuel pump, will this fix the
> problem, or is the check valve another part that needs to be replaced?
It's all part of the fuel pump module, so yes, a new fuel pump module will get you a new checkvalve, as well.