You can deactivate the serial number on your old PC, and then activate again on your new PC.
To deactivate the serial number on your old PC, click Help > Deactivate Serial Number.
Install the software on your new PC and use your original serial number to activate it. If you do not have an internet connection, please see this page on manual (offline) activation:
https://www.deskshare.com/manual_act2.aspx