Installed a new pressure tank today... Installation was done to the best of my knowledge. Now the pressure pump won't pressurize. We added about 20 gallons of water to prime it and nothing. The pump was working with the previous tank.

It's not supposed to take twenty gallons of water to prime the pump. You should have removed the plug at the top of the pump's impeller cage and poured in water until it would hold no more. Probably a gallon or two. Once it is full, that water level in the pump should hold steady. If it does not, then you have a foot valve/ check valve problem.

Jlisenbe nailed it! If you poured 20 gallons of water in the impeller cager then the check/foot valve is faulty. Although they both perform the same function a check valve installs on the surface while a foot valve is installed down at the well point, What do you have? Back to you, Tom