Non-refundable literally means that you cannot get back any amounts already paid. (See definition in MW's Learner's Dictionary)
But in the case of a hotel booking, which is often only paid after checking in or even at check-out, it usually has an additional meaning: You agree to pay a specified amount - up to the full amount of the reservation - even if you do not use the reservation.
It highly depends on what was actually agreed upon between you and the hotel (and maybe booking.com). This cannot easily be answered without knowing the contract.
So your best course of action would probably be to contact the hotel directly, as @pnuts mentioned. They should be able to waive the original booking ex gratia when you place another reservation with them. But be prepared for the case that they won't! As harsh as this may sound, this is the price you pay for - usually cheaper - non-refundable bookings!