If I haven't signed a new lease for 4 years, does the original lease apply now?

If you have been operating under the terms and conditions of the original lease that you entered into four (4) years ago, but that lease has expired, you are technically under a month-to-month lease under your state's law on the subject.

As to applicability of late fees, unless you signed an agreement making rent paid after ten (10) days as opposed to five (5) days of the due date subject to a late fee, the time period for the late fee to be assessed under the original lease of five (5) days would still apply not the ten (10) day period stated in the letter you recently received.