battery shutdown -> no radio anymore

Most radios are affected if the power is cut-off from them. This happens all the time when you'd take a car into the shop for servicing. They'll disconnect the battery for safety reasons and when you pick up your car, the radio has lost its memory - but it always works.

If yours is not working at all (ie: no power), then the fuse might have blown (I don't see why that would happen, but if it did, so be it...). Every car is different so I can't say where its located in your car, your Owner's Manual will have this info...

I kind of doubt it applies to the 360, but some new radios have a feature that if the power is suddenly cut off the radio will not work and needs to have the authorization code put in it again. This is a means of preventing people from stealing them and reselling, using in their own car, etc. I find it f_cking insane to be honest. I would just call the dealer and ask them, I doubt this is the case, but you never know.

Bret, You are right about the anti-theft device. However I find it unlikely that they would have installed a main cut off and then have to recode the radio unless there is a way to recode it in his owners manual. Each car may have its own code.