[Radioroslyn]

For starters read this before plugging in the radio the first time:
http://www.philcoradio.com/tech/plugin.htm
http://www.antiqueradio.org/powerup.htm

Diagram can be found here http://www.nostalgiaair.org/Resources/617/M0013617.htm

here's an article on changing / replacing the capacitors.
http://antiqueradio.org/recap.htm

Hope this helps.
The humming/buzzing might be due to a leaky filter capacitor that has lost it's ability to filter out the ac ripple from the power supply.. I'd really start by the basics and replace the electrolytic caps before trying to get stations.
Terry