1) your miniDIN wasn't corroded. You could solder that back on
2) Those inductors are hot because there's something drawing too much current. (see 4)
3) That diode looks cooked and seems to have reflowed itself a few times.
4) You probably have a short downstream of it
5) Please don't start yanking parts at random without understanding the circuit around them if you have any intention of restoring the machine. You could break something worse.