I guess you want to transfer the HDD to the new PC and boot from it, but you can't move a running OS installation from one computer to another, and the current install was done on a different computer, which means that the processor and chipset drivers installed will be different from those needed on the new machine
The OS installs some drivers during the installation, moving the drive to another PC after could therefore make it crash or make the installation a drive mess that will slow the thing even further. So it will really make no sense unless you plan to always have the external drive boot to the same motherboard and system and it will only work on your system.
Additionally, you will have to reinstall most of your applications as well because of the missing registries.
Hope this helps and feel free to ask any questions you may have.
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