Burned element on a turned off DE2 Board

Unfortunately, the damage may be larger than it seems at first look.

There's a DE-2 schematics with the DE-2 documents, the said part is L4 on page 20 (Rev. 2.0), it's the inductor of the 3.3V buck converter. It's very unlikely, that the inductor get burnt without other parts being defective before, particularly the SMPS chip U22 has a current limit. The inductor may get overheated at this current limit, but most likely not immediately burnt. So U22 can be expected to be damaged too. Finally, if U22 has a short, the 3.3V supply would be most likely driven to higher level. In this case, the board would be most likely done.

Also S18 is apparently damaged, otherwise the board couldn't be powered in off state. The wall adaptor may be defective as well.

L4 and U22 are parts available from many catalog distributors. L4 is s 47 uH/3A 1/2" square shielded inductor, U22 is a common National part. As a first try, I would connect a laboratory voltage supply and feed a low voltage (1 .. 3.5 V) at the input to check the state of the possibly affected components.