The Case of the Missing Software

When my XPS-8100 HDD failed, I replaced it with a new HDD and reinstalled the OS from the flash drive that came with the desktop. I'm trying to locate the starter Microsoft Office Home and Student 2010 that came pre-installed with the computer. There's a shortcut in the start menu but the app itself is missing. If I click, I get a pop-up request for an activation code--the 25-character product key--that of course I don't have. Microsoft says Dell should be able to find that key; the folks at Dell say there never was such a key for their pre-installed software. Which one to believe?

I figure the activated Office should still be in the computer, or in the flash drive. The folks at Dell can't--or won't--tell me where the software is. They know only that the computer is out of warranty and past its support expiration date, so I should buy a new Office suite or use a free substitute, which may be pretty good but in some important ways ain't the same. I keep saying I'm not looking for support; I just want what was part of what I paid for and now has been taken away.

Shouldn't the app that shortcut is meant to lead to be on the original flash drive? I can open the drive but can't discern anything understandable (to me). On a portable HDD I have a Windows Image Backup of the whole shebang from the computer's earliest days on Earth; it contains two Hard Disk Image Files but I'm afraid to go too far into those, or into the Recovery file that's also on the portable lest I mess up the HDD replacement and reinstallation that, somewhat to my own surprise, I've managed to pull off. I don't want--or need--to reinstall from those, since I've already reinstalled everything from the flash drive. Or everything except that elusive starter edition of Office.

Should that missing already-activated Office be somewhere I can recover it and put it back to work? Or if there was a product key, how do I find it? What should I look for, and where? Maybe on the original, now-deceased HDD? (You can tell I'm getting desperate.)