We're really sorry for the trouble. Have you created these presets on a specific image format? The images you have saved in external hard drive are different format?
Have you included any specific default profile while creating these presets?
Are you saying that when you are in the Develop module (assuming these are Develop presets) looking at a file on your internal hard drive, you can see the presets? But when you look at a file that's on your external HD you can't see the presets in the Develop module?
If a preset includes a raw profile (if you checked ‘Treatment & Profile’ when you saved it), then it will only show if you have selected a raw file. If you have selected a jpeg or tiff, it won’t show. And if that profile was camera-specific, then the preset will only show if you have selected a raw file from the same camera.