Just ruminating here:
The fact that it happens only to certain files must mean something. Evaluate what is different between those that work and those that don't. Particularly about their pedigree--who created the ones that won't open, when, with what application, etc.
Were the failures ever part of a CSV or other type of import or export?
Did the failures possibly go through a "save as" process at some time during which they were given another extension, purposely or accidentally?
Can you get the failures to any other Excel 2007 system to confirm if it fails there? You can send me one if you want.
There is such a thing as a macro virus. Do at least some of the failures have macros?
Poking in Explorer means just that. Open Windows Explorer, navigate to a failure, and see if it will open when you poke it with a mouse.
Windows safe mode: press F8 when booting, before you see the starting windows screen. F8 can be cranky. Try pressing that key maybe once per second. See if the failures fail when in safe mode.
Pick a random failure. Copy it to another folder. Try to open it from that folder. If you fail, manually change the extension to xlsx and try again.
For that matter, open a new Excel file, give it a name and go to "save as" and notice the "save as type". You can save Excel files with a jillion extensions. How many of the failures may have been saved with some oddball extension at one time or another?
Off the top of my head, pound that google search page in my prior post. You can't be the only person to run into this.
I certainly do think you could use a virtual PC on your Windows 7 box and run XP in that virtual PC. It might work, but would leave unanswered why they fail now.
I have very little experience with setting that up. Did it once 4 months ago for a few hours but don't recall details. You download a couple of apps from MS, install them, and configure. It isn't rocket science. If you wanna do that, search this very site for a tutorial or start or search for another thread "Need help setting up virtual PC to run Excel 2003".
Re virus: I'd say it is quite unlikely, but you never know. Default good app for that type of thing is a combination of Microsoft Security Essentials (or any good anti virus app) plus a scan with Malwarebytes from Malwarebytes.org. Download their free scanner, go to update tab, update, go to scan tab and do a full scan. I think you should also be able to scan random files with a right click.
Google a bit on macro viruses if the failures have macros.