If the lights flash,the remote works. What you actually have is a locking pump that is not doing it's job.
I am starting to suspect water intrusion in the trunk - both the lock system and top system are controlled by modules in the wheel wells - if water gets in, it can damage modules back there.

IT is not uncommon for water to get in if the car is left outside a lot. It should NOT happen but it does. A leaky rear window seems to the be most common culprit.
To check this, you must remove all the trim from in the trunk (the rivet things just pop out). Once you do that, it's EASY to see if water is pooling or sitting in the wheel wells.

Top controller is in the driver's side wheel well. Locking modules are in the passenger side wheel well.