Try this...
Think back to what was the very last thing you did under the hood.
If it was plugs and wires, could you have crossed two wires ?
I know you said the battery is new, but that doesn't mean anything.
If a cell in the battery shorts out, it can cause all kinds of weird problems.
I had a battery that was just over 2 years old short out.
If you think it may be ignition, while the engine is running, hold a portable AM radio under the hood area.
If any of the wires are bad, you'll hear it in the radio.
