I see the problem. You put the chips in the wrong places. The 74HC595 is supposed to be on the left, and the 74LS247 is supposed to be on the right. The chips are not the same! The chip numbers are printed on the silkscreen so that it was clear.
The regulator is hot because the circuit is shorted in the chips. They are probably damaged.
Perhaps you will be able to unsolder the chips with some solder wick. If you have access to a hot air gun, that will be best. Difficult problem….