My 89 F-150 won't start. When I turn the ignition there is just a humming or buzzing sound. I put on a new solenoid switch and had the starter checked out. I did notice the buzzing coming from the solenoid switch. Also does the same thing when I try to blow the horn. The interior light is only on when I have the battery charger hooked to the battery. I believe the battery has a full charge on it though. Any ideas?

. Remove and fully charge the battery.

. Clean battery and cable connections. Ensure connections are tight.

. Inspect condition of the cables.

. Clean main ground, solenoid, and starter motor connections.

. Check all under hood and under dash fuses with a test light or multi-meter.

This link may help:

https://www.askmehelpdesk.com/cars-trucks/faq-how-troubleshoot-repair-maintain-hondas-selected-other-vehicles-46563-3.html#post235560

My bet is that the battery is bad.

Yup. Bad battery.
You may feel as if your battery is fully charged, but it may have a bad cell. Usually, only specialized testers can verify that.
If your battery has any warranty left on it, have it exchanged.
If your battery has been in service for say 3 to 5 years, I'd try a known good battery. If it resolves your issue, buy a replacement battery from a reputable supplier.

Battery or cable ends