It could be the unit itself, or its fuse (may be in the fuse box as "Radio" ). I'd start with the fuse - remove it, check it, reinstall it. At worst, this will clean the contacts and point to the radio as a possible culprit.
It would also be an idea to try attaching a wire from the stereo chassis to one of the dashboard mounting bolts, the earth to the stereo has been problematic in the past.