You need to Download Norton Removal Tool from the Following Link.
Once you have Downloadand saved it on Desktop then Doubleclick on the Norton removal tool Icon and run the Norton Removal Tool.
The Norton Removal Tool uninstalls all Norton 2008/2007/2006/2005/2004/2003 products and Norton 360 from your computer. If you use ACT! or WinFAX, back up those databases before you proceed.Follow the on-screen instructions. Your computer may be restarted more than once, and you may be asked to repeat some steps after the computer restarts.
once the uninstallation compleates the You need to restart the computer and reinstall the Norton 360 on the computer.
Follow the Instructiions to Reinstall Norton 360 2.0
1.Do one of the following:
If you have the installation CD, insert the CD into the CD-ROM drive, and then click Install Norton 360
:-If you have downloaded the product, double-click the installation file. Unless you saved it elsewhere, the installation file is on the Windows desktop.
2.Read the License Agreement, and then click I Agree
If you do not click I Agree, you cannot continue the installation.
3.Follow the on-screen instructions.
Once the Installation is compleate you need to Enter you Activation key and it will automatic Activate it, after the Activation you need to run Live updates to Update Norton 360.
You can do the same on Both PCs.This will resolve your Issue.