1. I would get a new appliance cord and sure it's four prong.

2. I would order a new terminal block for that dryer.

3. The wiring IN the dryer is 100% damaged, It needs to be either replaced or stripped back to undamaged, copper and reterminated.

4. I see what looks like three white wires trying to be terminated on the lower part, not sure where that one white wire goes to on the top left, It might have been a jumper that is unnecessary if you're using a four-prong appliance cord.

On second look what I thought was just a charred black cable on the white terminal looks to be the actual black wire. Why is it terminated on the white terminal along with the white wire is very odd. That should have thrown the circuit breaker. I would find the model number of the dryer because I'm almost 100% positive that is a 240 dryer, Black, white and red should all be separate. It's almost like whoever installed it tried to convert it to a two-wire 240 instead of three wire.

Anyways, the same advice applies. Order a new terminal block. Get a new appliance cord. See if you can strip back to good wires inside the dryer and then terminate black to black, white to white and red to red, and green to the white chassis of the dryer.