the 1st step would be to look around the key that has the problem, although your problem too me sound compound, as the ducky should have n-key rollover and so one shorted switch should not disable 2 columns. the easiest thing to spot though would be that shorted ctrl key, look around the switch pads for a solder bridge, and maybe if you have a multimeter test if the diode is good (should only conduct on way the multimeter should display an overload one way and a low resistance the other) as if overheated diodes can fail, and from what i have learned the solder ducky uses is rather high temperature, if you used zealPC switches they are rather sensitive to temperature too so maybe if you stayed on too long the plastic holding the contact melted. as far as the keys not working go i would guess that it would be a lifted pad, but as the columns seems to be on the other side you may need to test with a multimeter and a piece of wire to check what connect to what and what fixes what, for example is your windows key still works try to bridge it to A for example and see if it restores A or more.
maybe someone with more experience of the ducky could help you better