My bets are on the old yeast being the culprit. If you want to keep yeast that long, you need to use sterile practices and keep small amounts of yeast. Once it has been used in brewing yeast picks up contaminates. Good practices keep the level small enough that it doesn’t matter even if the yeast is reused. But once you store the yeast for an extended amount of time you give bacteria a chance to feed on the nutrients in the slurry and their population will grow.
making a starter with old yeast may give you more fresh yeast cells, but doesn’t remove the other organisms. And if you make a starter from the whole old yeast sediment you’ll also get a lot of autolysis (dead yeast) products that you don’t want in your beer.
Kai