My Hard Drive failed, but I was able to extract my lightroom folder with my photos and place it on an external hard drive. Is there a way for me to import the photos from this folder into lightroom on a new machine and maintain my edits that I had made?
You do not need to re-import the images.
You need to open the same catalog with edits and relocate missing images.
Refer this article for steps : How to find missing photos in Photoshop Lightroom
Chetna's response is good for running LR off the external drive.
If you prefer to use an internal drive, just copy the catalog and images to the new internal drive, then "relocate" the images using Chetna's link.
Thank you Chetna & ManiacJow it worked for me!