Have an 04 honda odyssey EX-L I bought that had possibly sat for a short while. It wouldn't start but would take a jump instantly and runs perfectly fine. I took the battery to be tested and it was bad so I put a new one in it. As soon as I put the new one in all it does is click one time and will not start. It doesn't take a jump and I have had the new battery retested and it is good. All lights, dash radio etc work fine with the new battery. Still just clicks one time and does not drag or dim the lights or anything. I feel it's a fuse or something small that I have missed but wanted to see if anyone had ideas before taking it into a shop. Does anything need reset? I have looked at SOME of the fuses and none seem blown.

 

One click and nothing is sometimes a sign of low power or high resistance.
Clean up all the battery terminals and ground strap to chassis.

Then, there is the ignition wire that goes to the starter solenoid.
Sometimes the connector will have high resistance and prevent the starter from running.

If it still doesn't crank then put 12 volts to the starter solenoid and see if the starter will crank
If it does then try doing the starter relay by pass test.
That will let you know if the issue is with the load side or the control side of the circuit.