What could cause the hot water not to work after replacing a water heater?
First step is to assure all valves are open, including the main supply valve. Do you have cold water at faucets? 

Second check would be to open the bottom drain on the water heater to see if any water has entered the tank.  This will tell us if water is reaching the tank or stopping at the tank.

Do you hear any air passing at the faucets when you turn them on?

Are the connections threaded or solder? Not that makes a lot of difference, but will make it easier to trouble shoot if they are threaded and need to be removed. 

When you installed the heater, did you remove all the plastic pipe plugs that are installed for shipping?