Conflict: Everyone just trashes this dog who has sat on the dung pile for years. The problem is that the dog is too old to really move. He recognizes his master somehow but cannot move to him.
Resolution: Having finally seen his master and known that his master is alive, the dog dies.
Conflict: Odysseus as the beggar gets to see the men at work in his home eating and having a great time. Antinous throws a chair at Odysseus which enrages Telemachus. This conflict helps Telemachus in one regard, it grows his rage, but he is not to yet use it.
Resolution: Telemachus' rage gets to build for a future fight. The scene settles and is left for now.