I need help to repair my external hard drive

(1) My External Hard Drive finally stopped working. Whenever I tried to use it, I would only get variants of, "Time Machine couldn't complete the Backup to "My Passport for Mac", or "The backup disc is not available".

(2) "No problem," I thought. "There is no problem with my computer, so I'll just buy another external hard drive," and I did.

(3) About this time, I partitioned my computer hard drive to enable me to run both Snow Leopard and Mountain Lion. I did this with step-by-step instructions by Apple technicians.

(4) I now find that I have lost a considerable number of files, including those that I value most highly.

(5) I now find that I need the files in my old, abandoned external hard drive, and it seems to me that the easiest way to access those files is simply to repair it.

(Here's what I've tried so far: (1) Disc Utility Repair. Didn't help. (2) COMMAND-R start. This produced a window with the following entries: Restore from Time Machine Backup, Reinstall OSX, Get Help online, Disk Utility. It seemed to offer hope, but I couldn't highlight any of them, and the "continue" command was dimned out. Where do I go from here? Data recovery is the solution usually offered, and I've alwys wondered why. It seems to me that fixing the external hard drive should always be the first thing to be considered. Data recovery is expensive, and fixing the external hard drive might be cheap.