Starter Doesn't Turn Over

I have a 1998 Volvo xc70 wagon. When I turn the key to start, nothing happens. There is no clicking noise, no starter spinning noise. Just silence. The battery is nearly brand new and I tested it independently and it’s ok. Plenty of spark and the headlights are bright. There is also full voltage to the solenoid main voltage terminal. I disconnected the wire to the starter trigger terminal on the solenoid and connected a voltmeter. The measurements seem odd: 10.4 volts when the key switch is "on" and 0 volts when it is in the "crank engine" position (both in park and neutral – 0 volts in all other positions as expected). When I apply 12 volts to the starter directly it spins but doesn't engage. When I apply 12 volts directly to the starter trigger terminal on the solenoid, nothing happens – no clicking or anything. So what is bad - the ignition switch, solenoid, or some combination?