Are these the same?
It worked once.
It worked at one time.
It worked in old times.

Question

Answer

It worked at one time can imply that although it worked at one time, it does not work now.

Answer

1: can have two meanings. One of them is similar. But it can also mean 'It worked one time (and only one time).
3:  The meaning is clear, but it isn't very natural. "It worked in the old(en) days" is more idiomatic, or "It worked historically".