Your title "no power to the ignition switch" says you have checked to see if there is power
TO the ignition switch.
To reiterate what others have said:
1. As said, the ignition switch has nothing to do with starter not turning over. Batt pos cable goes to a big push button switch on top of the starter. Call that the starter switch. Foot stomp pushes lever to engage pinion gear on starter to flywheel gear. Foot lever also pushes on starter switch button to spin starter.
2. As said, the lights are not wired thru ignition switch.
3. Gas gauge is thru ignition switch.
4. Ignition switch turns on gas gauge and coil.
We can see that the problems are not ignition switch related. We can see that two are items are on a direct source of voltage, one is thru the ignition switch which is on a direct source of voltage. (Battery/generator or cables). You may not have any electrical components working.
First thing to do is put a volt meter on battery for a baseline. Should be about 12.6V. If you are not good at electrics and don't have a meter,You can jump it to see if troubles go away...or have it tested. Some FLAPS don't have the right tester. Some have the right tester but the wrong tester'er.
. A guy at Autozone finally knew what he was doing recently. Oreillys not so much. I realize you said new battery. So logic, which is just an educated guess, says cables. Battery first!
Costco, where I buy all my batteries, now tests them when you bring them back for refund.
