The usual first step we get all LSI Hammond owners to go through is to unplug, clean and reseat every internal connector. You can use Caig DeOxit on the connectors. Problems with these connectors are the root cause of many a problem in these Hammonds, we tend to call it 'LSI Disease'. Even if it doesn't cure the problems you have right now (though it might well do so) it's good preventitive maintenance.
See what you've got working when you done the cleanup.