this didn't happen, exactly when the battery was replaced? It happened later? If yes, then battery installation was not the problem...
Go to your fuse block, turn key to on, not start.....check all fuses for power and check to see if any are blown...replace blown ones....if you have more than one fuse without power to it, could have an ignition switch problem.....
Does the rheostat work on the lights of the dash? In other words, does the dimmer work? Have any affect on any of the lights to the radio/HVAC head?