2002 Honda Accord hard starts. Sometimes?

Ok, as an amateur mechanic this is definitely a head scratcher.
vehicle:

2002 honda accord LX 3.0l, 120,000

The engine starts with one turn of the key sometimes. Other times, it takes two turns of the key and the engine will be turning over for about 5-10 seconds before it fires. I'm thinking maybe a crankshaft positioning sensor? I was also thinking maybe a weak battery or starter/solenoid, but it has a new battery, and as far as the starter goes, sometimes it starts on the first crank of the engine. I've looked everywhere but haynes/ chiltons manuals and that's my next stop. Any help would be GREATLY appreciated.