The elemental king should automatically start a conversation as you approach (even if he is in the middle of a fight). In that conversation, you can either convince him to give you the teleporter piece (after which he turns hostile), or demand it (in which case he turns hostile, summons help and drops the piece when defeated).
If he will not speak to you, can you attack him (perhaps with splitting arrows or an area effect spell that does not need a target), and see if he drops the teleporter piece?
You need the quest entry from the billboard to get into Serrick's building to talk to him, so the missing entry may just be a glitch (or be filtered). Do you have the latest
patch installed? (1.47 fixes a couple act 3 quest log problems)