If you're using a 12V radio powered by the converter and you have an older converter, it may be putting a lot of noise on the 12V line. The battery can help clean up some of the noise. A newer converter that produces cleaner power would help a lot in this case. (Turning off the converter and running the radio off of battery power would also fix that problem.)
Poor or improper grounding somewhere can cause a hum.
AM radio is much more susceptible to interference such as hum than FM radio. If it's an AM broadcast and you're near something like high voltage power lines, you may simply be out of luck.