Just because the battery is new doesn't mean its good. Test it with a meter, it should say at least 12.9V (yes that is correct). If it does, then have someone crank the car while you have the meter on it. If it drops below 11.5 volts, bad battery. Now if it doesn't really move at all, then you have a connection issue somewhere. Check battery connections first, clean them if they need it. Check cable for corrosion as well. Change starter relay, just because it clicks doesn't mean its actually working. Thats really all it come down to its a really simple system.

Battery not charged ?

Hooked up wrong ?

Loose cable clamps ?

Check battery connections and starter connections.

How do you do that