Another reason you may not be able to do online check-in is if any part of your itinerary contains international travel.
It won't claim you are denied for security reasons, but rather than online check-in isn't available and that you'll need to see a DL agent.
This, i presume, is because of the things DL has to do on International legs, like seeing your passport, checking baggage weights, and other international pparticular things.
If you're travelling domestically, you shouldn't have a problem..
Steve G