Diagnosis
If the LED is completely dead with a confirmed fresh CR2 battery, the electronic monitor unit is probably faulty. These are simple gadgets, and the circuit or the button can fail, especially if they've gotten wet inside.
How to Fix It
Confirm the battery is installed correctly (positive side facing the button/up). Try pressing the reset button firmly with the battery in. If nothing, the monitor is dead. You can buy a replacement electronic indicator (PUR calls it a Filter Monitor, part # varies) separately. It snaps onto the filter head. No tools needed.
If That Didn't Work
Before you write off the monitor, check for corrosion on the battery contacts inside the compartment. Clean them with a cotton swab and a little vinegar or rubbing alcohol. A film of corrosion can block the connection.
Heads Up
The filter works perfectly fine without the electronic monitor. It's just a reminder. You can track filter life manually (100 gallons or 2 months) if you don't want to replace the monitor. Water will still flow and be filtered.