Diagnosis
This is a total clog or a stuck diverter. Either the filter cartridge is completely blocked by sediment, or the internal valve in the filter head isn't sliding over to open the flow path to the filter.
How to Fix It
First, switch the lever to "unfiltered" to get water flow. Then, remove the filter cartridge. Try switching the lever to "filtered" with the cartridge out. If water sprays out of the empty housing, your old filter was clogged. Install a new one. If no water comes out even without the filter, the diverter valve inside the head is stuck.
If That Didn't Work
For a stuck diverter, perform the vinegar soak fix described in the "stiff handle" problem above. If that doesn't free it, the diverter mechanism is likely broken and the filter head needs replacement.
Heads Up
If you have very sandy or silty water, a standard filter can clog incredibly fast. PUR makes a "Premium" filter with a sediment pre-filter layer (like the PPFM900S) that's better for that, but it still needs changing more often.