Take a look at the original sentence again:
My cat Buster is always tipping over the garbage
can then he searches through the trash for
milk jug caps, which he bats around the floor, the cat version of playing
ice hockey.
You wanted to fix it this way:
My cat Buster is always tipping over the garbage
can, but then he searches through the trash
for milk jug caps, which he bats around the floor, the cat version of playing
ice hockey.
A perfectly legal move in writing is to connect two main clauses with a comma and a coordinating conjunction like but. The important thing to remember, though, is that you must choose a coordinating conjunction that logically connects the two clauses. In the example above, but, a transition that shows contrast, is illogical.
You might want to consult the rules for fixing comma splices and fused sentences.
Go back to the sentence to try again.