My 1995 Dodge Stratus won't start

A new battery this year. Key in ignition engine rolls over an nearly starts as usual, but with 2nd try, it fails to do anything! No idiot lights on dashboard, nothing. Headlights work fine, battery apparantly works and may be fully charged (I think so). There is no clicking to indicate a partially charged battery - it is just DEAD!

“No dash lights” would indicate that the ignition switch isn’t …er…switching.