How is the EHD formatted?
Verify that the Finder preferences are set to show external HDs:

If it is, toggle it on and off a couple of times, reboot if necessary.
Next, boot into Safe Mode, Mac OS X: Starting up in Safe Mode, and see if it shows there. Reboot normally and check again.
Download and run Etrecheck. Copy and paste the results into your reply. Etrecheck is a diagnostic tool that was developed by one of the most respected users here in the ASC and recommended by Apple Support to provide a snapshot of the system and help identify the more obvious culprits that can adversely affect a Mac's performance.
