Hey there, @billydavis!
Unfortunately, you won't be able to load old software from a different system to your new rig. Moreover, the fact that this Win 7 OS belongs to a different PC won't allow you to boot into the new one. You need a new genuine Windows installation/activation because the operating system is tied to the motherboard of the computer, whereas the hard drive is just a carrier for the system files. You shouldn't face any issues with a brand new installation on the new computer, but I'm afraid you won't be able to use the old one.
However, you can still back up the data from that drive somewhere off-site (to an external HDD, cloud storage, etc.) and then plug it as a secondary HDD in the new system and use it as a data drive for your files. Yet again, this will still require you to re-format and wipe the HDD clean before you can use it like that. The backup is essential before the upgrade, otherwise you will most probably lose all the personal files on the HDD from the old PC!
Let me know if you have other questions. Hope this helps you, though.
SuperSoph_WD