What does he do if the old jack has a different number of wires attached?
I’d go for the power cord replacement. But dryers have a standard receptacle configuration, which is three prong, IIRC. Sounds almost like it was wired for a range or something.
Ranges and ovens have different configurations, because they are often set up for even higher amp service than a dryer.
That matter could be dealt with by trading down the breaker for the circuit if you think it’s necessary.
The main point is to get two hot wires to the dryer, one neutral wire, and perhaps one ground wire as well. The ground wire, if connected through, would also connect to the metal frame of the dryer, otherwise the neutral wire does that.
Under no circumstances should a hot wire be allowed to substitute position for a ground or neutral wire. If you don’t know what you’re doing, it could be the last mistake you make.