Tell me the exact version of Lightroom installed on your computer. It's under Help/About. It seems to me that if your album has small images then you must have been using Lightroom Classic, which involves a catalog on the local computer. Does that sound familiar?
You would need the catalog from your old computer. I'm assuming that, on the old computer, Lightroom Classic was managing the images on the external hard drive. So if you are able to obtain the catalog that you were using previously, and the external hard drive still has the same drive designation, if you open that catalog Lightroom Classic should be able to locate all of your images and should be able to synchronize with your cloud images as well. That is, if I'm understanding everything correctly.
Additionally, the cloud version you are using at version 3.4 has been upgraded and is now at version 4.0. You might also want to check to see if your creative cloud application manager is up-to-date.