There is a bug during the Silver Shroud questline in which it fails to progress after you kill AJ. After you agree to become the Silver Shroud, you're supposed to kill Kendra first, but this part will be omitted. Instead, you will be dealing with Delancy and AJ first. After you've killed AJ, the objective of the quest is to listen to the radio, but the radio will only broadcast regular episodes, and the quest will not progress. You can fix this by locating and killing Kendra by yourself. The wiki page also mentions this bug.
This is probably because you have accpeted Charlie's quest to clear out the warehouses but have not completed it. Because Charlie is also the one you have to talk to to obtain the Kendra mission in the first place, this might cause some sort of conflict.