Combine two independent switches into 3-way?
If you use the hallway circuit to power the three-way circuit, you must run four conductors (plus ground) between the two switch boxes. 



(If you needed to use the dining room feed you would have to run five conductors.)

With this circuit, you abandon and cap off, or remove completely, the feed cable to the dining room switch. You also abandon and cap off, or remove completely, the useless stub cable to the terminated j-box. I have omitted those cables from my diagram. 

I have omitted the fault ground wires from the diagram, but don't omit them from your house. 

Using the hallway light j-box as your power source is safer than using the dining room switch j-box. With power coming from the old dining room end, the two-gang (the one with the hallway switch) would have live wires from two separate circuits. A future electrician might not know that he has to flip two circuit breakers to make the box safe to handle.