Welcome to the forums.
I don't have personal experience with W7, but I believe it has an "XP Compatiblity" mode.
I would strongly recommend that you use that for CS3 (a 32bit application) for best results.
You might want to take a look at this THREAD. Near the bottom, a poster lists the build of Win7, that got his Adobe packages up and running. Some earlier builds seem to have real issues with Adobe programs that had run until two builds were applied. They seemed to break all things Adobe.
I don't want to waste debug time if there is a basic incompatibilty between CS3 and the OS or 64 bit version.
CS4 is the first version 'approved' for 64 bit use. It's well worth the upgrade.
My problem with capture seems to have been corrected by an update to the motherboard device drivers.
However, I did first try the "XP Mode" suggestion. XP Mode runs as using "Virtual PC". This two step approach requires that you first install the Virtual PC application on Windows 7 and then install "Windows-XP-Mode" as the OS on a Virtual PC. Before that, the motherboard must have "Virtualization Technology" turned on. This seemed a little cumbersome for a long term solution so I stopped before installing CS3 on the "Virtual XP Machine". I did a little more shotgun experimentation including driver updates and found that capture had begun to work.
To be sure of the solution, I did a fresh install of Windows 7 (overwriting previous disk contents), motherboard driver updates, and CS3 install (with updates). Capture is working for both DV and HDV modes. However, do note that my motherboard does now have Virtualization Technology enabled. This may or may not be a factor.
I have also noted that there is also an "XP Compatibility Mode" option available for applications (that is different from Windows-XP-Mode). Windows 7 presents this option by right clicking on the shortcut and selecting Properties/Compatibility.
Hope this helps the next person to stumble down my path.