Car won't start; battery good

My '96 Mercury Sable won’t start. The battery is fairly new and the fans and lights work, but the starter won’t turn over. All I hear is slight hum, and nothing happens

The hum may be the starter motor working, but if the solenoid is faulty the starter gear won’t engage with the flywheel and spin the engine.

How new is a “fairly new” battery?

Also check insalated part of hot wire at battery.
Enough power gets for lights but not enough for starter.

the battery may not be good, even fairly new, have a bad connection. Needs to be tested under load, clean terminals, etc. The alternator may be failing to keep it properly charged so output of it should be checked…expect 12.4 Volts at battery at rest then start engine and test, the output should be around 14.5 Volts If less, you need new alternator. Starter could also be bad, No solenoid engagement or you would hear clicking. Start with Battery and alternator first, then check starter.