What type of licensing are you using (Single Use, Concurrent Use or Named User)?
You are allowed to install ArcGIS Pro in three different computers, so that should not be a problem.
Hi Raymond Baptiste ,
Below the process to activate a SU license:
However, since your computer crashed you will most likely not have "returned" the license and there might be a problem to activate the license (if you still have it) on a new computer. Probably best to contact Esri Support and let them see if they need to reset the license so you can activate it on your new computer.