When a radio station always plays music with no commericals, how do they make money?

In the UK, the BBC Radio stations are commercial free. They get their money via the Licence Fee

what is the best way to get a 1000 watt am station in a town over 10,000 to start generating income?

Thru donations. Those are usually stations that have a certain listener base that would gladly support the station with their contributions so that they can listen to those programs that only that station offers. PBS (the tv station) works on those grounds and, usually, so do any of the stations that broacast NPR

We have a favorite cable station that we watch when we watch movies and it is TCM..Turner Classic Movies. There are never any commercials..no interruptions. I don't know how they do it but they've been doing it for many many years. So however it is they make money I expect the radio station does the same thing..maybe contributions by grateful listeners? :)

Those were run by government for public, under services

Pledge drives and sponsorships. Periodically, they ask their listeners to contribute financially.

They are probably totally automated (no personnel), satellite (subscriptions pay for the overhead), or they are sponsored by a company who doesn't require the commercials. If you're speaking of music played in elevators, and businesses, the business pays to have it piped in.