Radio is controlled by the tuner and the amplifier (is you have DSP). All screen output is controlled by the Nav unit.
If your screen is gray there are only 3 causes: Bad boardmonitor, interference/fraying of the signal cables, or a bad Nav unit.
If the radio cuts out there are only 4 causes: Bad boardmonitor, intereference / fraying of the power cables, bad tuner, or bad amplifier. If it also cuts out while playing a CD then we can eliminate the tuner (unless you have DSP, in which case we eliminate the amplifier).
The only common thread in these failures (since you've already changed the battery) is the boardmonitor. If, for some reason, it were to send incorrect signals through the iBus and have a screen failure it would explain your issue.
Unfortunately, the only way to diagnose is to put your nav into someone elses car and see if the problem recurs...