SOLUTION
Here's what finally worked for me (thanks to a post by RagnarX, on Nov 12, 2009
http://en.kioskea.net/forum/affich-17997-ipod-not-detected#p121082). It may work for you, too, if your system is similar to mine* - without your having to beg Dell, Intel, Microsoft or - perish the thought - APPLE, to provide any form of customer service.
#1 Uninstalled iTunes and every application with Apple anywhere in its name
Used Control Panel (in Win7) uninstaller for iTunes
Used Revo uninstaller for everything else
Ran CC-cleaner to scrub system further
#2 Shut off firewall and antivirus
#3 Rebooted
#4 Connected iPhone to a friendly USB port. Win 7 recognized it as an iPhone, as usual
#5 Reinstalled iTunes x64; designated that installation files be copied to C:/Program Files, not C:/Program Files (x86). Probably irrelevant.
#6 Opened iTunes and prayed
#7 iPhone appeared almost instantly, along with most of my music files, Apps, and photos.
#8 Synced successfully.
#9 Turned firewall and AV back on.
Total time required: about 35 minutes
*iTunes ver 9.0.2.225
iPhone 3.1.2 (7D11)
PC: Dell Studio XPS 9000 with Intel Core i7 920 2.66GHz 8M L3 Cache 4.8GT; 8 GB RAM
Operating System: Windows 7x64 Home Premium
Chipset: Intel X58
Motherboard: DELL, Inc. Model 0X501H