New Leviton GFCI outlet not working
I connected the line and load wires properly
Actually, you probably didn't. Not definitely - it could be a bad GFCI - but most likely the wiring is not 100% correct.

Turn off power.
Disconnect everything.
Connect only the Line wires - hot and neutral - and the ground wire.
Turn on power.
See if the GFCI receptacles work.
See if the GFCI test and reset buttons work.

Assuming all of that works, then connect the Load wires - hot and neutral - and see what happens. If at that point things stop working, then the problem is downstream - i.e., in the receptacles or devices connected via Load.
Keep in mind that with a non-GFCI receptacle, line and load are all the same. With a GFCI, you have to keep them separate and connect them properly or strange things happen.