05 Pontiac Montana acts like dead batter but won’t jump and with new battery just makes a click when I try to start it?

Either a starter that needs replacing, or a bad battery or starter cable.  I'd suggest towing it to your mechanic to find  out.

I would thing first about the battery cables.   Maybe your oil is way too thick.   Maybe it is REALLY cold and your block heater is not working.  Maybe your new battery is no good or not fully charged

Replace the battery terminals and try again.  No joy, get the vehicle towed to a garage. 

If the starter is not turning the motor over (cranking it) you either have a bad cable connection at the battery, the negative ground strap on the motor or a bad starter. Better hope it's a bad starter or else the motor may be seized up.

Corroded wire, reset ecm, bad starter, need amp test results

If it just clicks with a new battery, then check your battery connections. Make sure they are clean and tight.

maybe you should get a mechanic to check it out