My Galaxy s3 suffered from what seems to be the "sudden death syndrome". It had been turning off once in a while and wouldn't turn back on unless I removed and the battery and put it back in. But the last time it turned off it would not turn back on. When I connect my phone to the PC, the PC will make a sound recognizing the device has been connected but does not read it. When charging the phone to a wall socket, nothing happens. But if I remove the battery and connect it to either the outlet or the PC, the red led goes on. The battery isn't the problem though because I tried a different galaxy s3 battery and it did not work. I sent my phone to Samsung for repair under warranty but my question is whether they will be able to tell if the device is rooted despite the phone not turning on at all. Thanks a lot for the help!
If you can connect to the device from a PC then they will most likely be able to tell. It might not matter though because they might not look for that and unless they intentionally look to see if its rooted they will not know. Also like @Poldie said they might not legally be able to do anything about it depending on where you live.
They will know probably after they fix it. If you rooted it and used a different firmware on the device they can recognize the changes from it's previous memory.