No power, new battery

Assuming that you didn't just aquire it, it's likely either a faulty solenoid or starter switch. If you just aquired it, it could also be a bad or disconnected seat or brake switch.
To test the solenoid, put a voltmeter between the chassis or battery NEG terminal and the small terminal on the solenoid. Does it have 12V when you try to start it? No? you need to test the start switch and the safety (seat and brake) switches. Yes? Check the voltage on the 2 large terminals on the solenoid. One should have 12V all the time, the other should have 12V when you try to start. Does it? Yes? bad or disconnected starter. No? bad solenoid. Testing the safety switches involves testing the resistance (ohms) of the switch. It should toggle between infinite and around 0 ohms as you actuate the switch. If it doesn't, it's bad.