A hard drive with my Adobe leases was virus infested and destroyed before the Adobe products could be uninstalled. I have had to uninstall the 2nd computer install (laptop) in order to install on my newly constituted desktop. I would like to reinstal

Normally you do not have to uninstall anything, you only need to deactivate. You did not need to uninstall on the laptop, nor did you need to deactivate it.  If this is for the Creative Cloud then you should be able to install and sign in on the laptop now and it is likely to ask you if you would allow all the other installations to be signed out.  You can select yes which will clear all activations and then after the laptop is activated you can sign in on the new desktop again as well.