As far as I know its possible to upgrade the Nero software.
You need to download this from the Nero homepage and then have to use the serial key which belong to the version on the external HDD.
Here are some details:
http://aps2.toshiba-tro.de/kb0/TSB14034U0000R01.htm
But I’m not sure if you will be able to find out the serial if the Nero software cannot be installed… you know…
Did you try to copy the Nero file on the notebook HDD and then to start the installation?