I would start by explaining the problem to your VAR (Value Added Reseller) - the company who sold the license.
Ask your VAR for a home license.
A home-use license applies only to network licenses. If you are trying to use a standalone license, it is possible to install it on a second computer as a backup but it may not be used at the same time as the main install and 80% of the use for it must be performed on the main installation.
Either way, it sounds as though you could use some help from a VAR on solving your problem.
Sorry to just add to the chorus, but absolutely call the reseller - we have tools to view which licenses are activated on which machines, and can easily make a change (or instruct you on how/when you can use a home license).
You will have to go into the installation manager to change that serial number, and might end up having to download some components depending on what was active on your trial vs. your 'real' license, so try and leave yourself some time before you "need" that laptop for SW!