Check for the drive in disk utility on both computers, especially the first one.
If it's listed there, run First Aid on the disk. Do a verify and repair on it. Let the process complete. See if that will correct the issue or see what it will tell you when it's done.
To all users: If your data is stored ONLY on an external hard drive, then it is NOT a backup. A BACKUP is having the data stored in TWO or MORE locations. If it is only in ONE location, you don't have a backup at all. If the data is important to you, then have it stored in multiple locations to prevent data loss.
