You may need to use a better or sharper grinder. A good, sharp grinder (ideally a good burr grinder) grinds coffee into particles that are all the same size. A cheap or dull grinder produces a wide variety of particle sizes and the very small dust-like particles at the fine end of the particle size distribution block the flow around the larger particles, turning the layer of coffee particles into a barrier that blocks your pressing.
Press gently, there is no rush. Pressing hard actually compacts the coffee particles into a barrier, making it harder to press. You can try pressing down half an inch, then hold the plunger there and let the air pressure in the chamber do the pressing for you. Then after 5 or so seconds of waiting, press another half inch down and repeat until finished pressing.
If the above two points don't work, use a coarser grind until you get to where a minor amount drips through prior to pressing and slow, gentle pressing takes 20 to 40 seconds.