I have finally resolved this. The issue was with my version of Windows 7 Professional SP1 64 bit.
The solution was a "repair install" or "upgrading" the operating system to the same version from the installation DVD. Instructions for doing this are on the sitehttp://www.sevenforums.com/tutorials/3413-repair-install.html.
Apple iTunes Store Customer Support and the Apple Support Team provided friendly assistance. Diagnostics tests and files sent showed nothing was obviously wrong except there was an exception thrown by WebKit.dll in Apple Application Support. I knew this already. They said there was a Microsoft certificates corruption issue and should reinstall the whole system.
I ran sfc /scannow from an elevated command prompt (run as Administrator) several times and found two issues:
1. t2embed.dll could not be checked.
2. _isdel.exe was missing from C:\Windows\SysWOW64\InstallShield.
Issue 1 was probably caused by a workaround for the Duqu security vulnerability. User gn_id posted a solution for this on December 5, 2012 in this forum that involves running Microsoft Fixit 50793, please see http://support.microsoft.com/kb/2639417.
Issue 2 was probably caused by Malwarebytes' Anti-Malware. It led to deleting _isdel.exe from its quarantine. In November 2012, the program gave false positive reports for the "Trojan.zbot" (http://forums.malwarebytes.org/index.php?showtopic=117549).
sfc /scannow reported the _isdel.exe was missing and it could not repair the member file. I copied the source version of _isdel.exe from the installation DVD to C:\Windows\SysWOW64\InstallShield after extracting it with 7-Zip FIle Manager, but there was no change with sfc /scannow and iTunes kept crashing when I tried to connect to the iTunes Store. I could still update podcasts and apps, and sync my iPod and iPhone.
Finally, I decided to do a repair install as a last resort, short of upgrading to Windows 8. This keeps existing user files. I took a backup first of all files. The system rebooted about four times and you it rebooted from the hard drive, not the DVD. After this, sfc /scannow worked and iTunes 11.0.4.4 could connect to the iTunes Store and display its contents.
I hope this is useful to others with a similar issue.