I rolled my ira into a roth this year. the ira was 100% the result of a 401-K rollover into the ira many years ago. By definition the basis in a 401-K plan is zero...is this correct? That is, there is no way to have had a basis in dollars that went into a 401-K plan?

Generally you would not have any cost basis in a 401k plan.
If the plan allowed for after-tax contributions then you would have a cost basis equal to the after tax contributions.
When you rolled over the account, the plan should have told you if you had any cost basis, because you cannot roll over your cost basis.