After struggling to get Quicken to work at all with Windows 7 64-bit (see above), I finally solved the problem. It prints checks on my HP LaserJet 4P with no problems.
I would suggest that anyone having printing problems should first verify that they can print correctly with other software (such as Open Office, for example).
My problem with getting Quicken to display the Open File dialog without first crashing was solved per the suggestion of someone on a Microsoft forum - I reinstalled Quicken, running the Setup As Administrator and emulating Windows Vista. Note that my account on Windows 7 had administrative privileges, so I don't what tell telling it to "Run as Administrator" accomplished. I assume that the Vista emulation was what made the difference (I had reinstalled a few times before).
This was my first encounter with Quicken Tech Support after many years of using Quicken. They were not very helpful, sending me down a lot of blind alleys.