No, you will not be able to run that software under R2013.
If you can "lease" a computer for a few days (including from your friend), under the license terms you would be able to install your MATLAB release and toolboxes under your license. That might require that you go through the licence center to deactivate your current laptop before you can activate on the other system. Do what you need, and afterwards when your repair is done, reactivate on your own laptop deactivating on the one you "leased". Your friend must not have access to the computer during this time to fit within the license terms.
Note: each of these activations will count against your license transfer limits, so this will use up 2 transfers even though you are going back to your original system.
... Sometimes it is easier to just buy a second license.
