I bought a 2011 Mazda 3 from a private dealer two days ago and gave it a new battery, battery post terminals, spark plugs, wipers, air filter, oil filter, filled the power steering, and changed the oil. Went to turn on the car today, the lights came on briefly, there was 1 click, and then all of the power died. Checked all of the fuses (under hood and left side of driver), replaced 2, car still dead. Cannot move the gear shifter to neutral, so I can't try starting in that. The car has not had power since I tried starting this morning.

What else can I do?