There is nothing wrong with your Xbox; this is normal behaviour for a modified Xbox.
Please read this
discussion for more information about Xbox Live and a modified Xbox.
The safest way to use Xbox Live after performing the exploit is to uninstall the exploit. To do this, turn on the Xbox with the eject button to get into the ltools/MXM dashboard and find UXE uninstall. You don't need the Mech Assault game for the uninstall, but will need it to reinstall. XBMC will remain installed throughout this procedure.