Sounds like a loose connection - possibly in the power supply (DC voltage).
Does the static also happen on the AM band ?
If so, the loose connection may be in the power supplying the radio.
If positive side checks out ok - don't forget to check out the ground side -
all the way back to the battery.
I had a similar problem with an old buick once, and fixed it (after much
troubleshooting with a multimeter) by running a wire from the negative side
of the battery to a screw on the body - The lights stopped blinking - the
radio static cleared up - and all was well in the world.