Why won't Excel 2013 work as an "Open With..." program in Windows 7?

Finally figured it out. It was directly related to the switch from 32-bit to 64-bit. Poking around the registry I found the following key was wrong:

HKEY_CLASSES_ROOT\Applications\EXCEL.EXE\shell\open\command\(Default)

Within this key was the following "old" value:

"C:\Program Files (x86)\Microsoft Office\Office14\EXCEL.EXE" "%1"

When I changed it to the correct, new location for Excel, it started working immediately.

"C:\Program Files\Microsoft Office\Office15\EXCEL.EXE" "%1"

you're right on the mark, but mileage may differ..

That is, the correct registry value in my case is:

"C:\Program Files\Microsoft Office 15\root\office15\EXCEL.EXE" "%1"

And yes, it started working right away. Awesome!