Hi Welcome to Norton community!
Hi you could transfer your license from your old PC to a new one by contacting customer care!
https://www-secure.symantec.com/norton/support/contact/chat/norton-chat.jsp?chatexp=cs&dept=cs&pvid=&pid=cs&layout=
also Norton Does not usually Ask for net connection for uninstallations
as for Norton account goes well Few days back quite a few were not able to open it up,seemed that the Server was down or something similar!
If you really do want to get rid of Norton
then you could use the removal tool
http://us.norton.com/support/kb/web_view.jsp?wv_type=public_web&docurl=20080710133834EN&ln=en_US
Using removal tool without uninstalling the product from Add/Remove is not the right method please run the removal tool twice and restart prompted
hi if you use Identity safe please follow these instruction to back up and transfer license to new PC
1. Start Norton Internet Security.
2. In the Identity section, click Settings.
3. Next to Backup Identity Safe Data, click Configure.
4. Click Browse, and select the location where you want to back up the Identity Safe passwords.
5. Enter the filename, and then click Save. (The file will be saved as .npm format)
6. For added security, you can assign a password to this backup. After entering the password, click OK.
7. In the confirmation window, click OK.
8. In the Settings window, click OK.
After installing the NIS on your new computer, copy the .npm file from old computer to the new computer via CD/Pen drive. Then follow the steps givenbelow to restore it on new computer.
1. Start Norton Internet Security.
2. In the Identity section, click Settings.
3. Next to Restore Identity Safe Data, click Configure.
4. When you receive the warning message, click Yes to confirm, and then click OK.
5. If you have assigned a security password to the backup, enter the password. Click Browse and locate the .npm file which you want to restore.
6. Select the file and then click Open.
7. Click OK.
8. In the confirmation window, click OK.
9. In the Settings window, click OK.
(the steps provided are given by yogesh_mohan
all credits to him )
http://us.norton.com/support/kb/web_view.jsp?wv_type=public_web&docurl=20090821144746EN&ln=en_US
(this is the symantec link to backup identity safe)
hope this helps