You had already got best advices from Mitch and Coked; at this point try all you can, even holding water and blowing steam through; if you can get steam/water through and able draining through the pipe, then you are in good shape, especially if your is a bottom entry drum without distributor? Normally bottom entry are easily plugged, especially when draining.
ultimately what you are looking for is making sure what ever is in that gets properly cooldown to avoid any hot tar material igniting and causing more damages.
It could be a very serious situation considering the drum may still be full of resid due to very short time into coking; also, you have H&C, which requires further safety precautions during unheading; just be prepared for the worst and hope for the best. Good luck and lets know how did it go