Delete broken unrecognised external partition
I know this sounds insultingly simple, but have you completely unplugged and powered down the external drive and plugged it back in?

At the office, TM would periodically decide that the time machine disk was damaged and could not be written to. Restarting didn't fix it, even though it was mountable. Removing power to the device and plugging it back in fixed it and allowed it to be written to again. In both of the cases, they were LaCie drives. Give it time after plugging in, it could be doing a disk repair in the background before it shows on the desktop (can be verified by looking in activity monitor.)