I can see my device in `adb devices`. It shows up as "offline".
When it is "ready":

    $ adb shell
    $ su
    # reboot

This would reboot my device.
The exact problem is that my cellphone has been turning off on its own with no specific reason, so I was wondering if I could check the logcat to see the problem. I cannot start my device, I have to remove the battery and then start it, and when I do the log is empty...
But my questions here are:

 - If adb can detect my device why can't it reboot it?
 - Why can't I turn on my android device from adb when I can reboot it?
 - What does offline mean: is it turned on or not? (when it isn't usually it doesn't even show in adb devices)