Well, your while loop makes no sense, though I don't think that could break the program.
Are you sure there is something to stop the app in the end? You should also put the same thing before every exit() you use.
As I said, your while loop makes no sense.
'ch = 'X'' has no effect on anything, your not using letterCount anywhere...
Try this instead:
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while(!fin.eof()){
char c = fin.get();//get the char. You may want to use tolower here if you want this to work with capital letters too
if(c >= 'a' && c <= 'z')//check if its a letter. I think there's a function isalpha that does this
letterCount[c-'a']++;//increment the appropriate element
}