My old computer died last week. I now have a new Win 7 Professional 8GB ram, and 1 TB hard drive. I can see my Lightroom license key in my Adobe account.
How do I get Lightroom back on this new computer?
Assuming you had LR 5, then download and install the latest LR 5.6 update from the Adobe Updates page and enter your serial number when you first run it:
If you have an older version then find Lightroom / Windows down further on the page and install the latest version of whatever LR version you had. In other words there’s no reason to install the .0 version and then update to the latest version.
If you’re asking about getting back to your old work, then you’ll need to copy your catalog and photos to your new computer, or if they are already on an external drive then just make sure you assign the same drive letter to that external drive.