The H-P 3300c scanner drivers are 32-bit and do not work on Windows 7 x64.
The solution is to add on Windows XP Mode from Microsoft. This creates a virtual PC on your system that runs Windows XP. I have my scanner working perfectly this way.
The one difference is that you must attach the scanner to the virtual PC's USB driver. This is an extra step that's analogous to plugging in the USB cable. When you boot the virtual PC, go to the USB menu at the top of the window and select "HP ScanJet 3300c Attach".
As you know already if you have used this scanner with Windows XP, The H-P driver for the 3300c is somewhat brittle. Changing anything in XP can break the driver, making a driver reinstall necessary. When I start getting "undefined error 2117" I know it's time to reinstall the driver.
The steps to reinstall the driver (note these steps are all performed with the XP system on the virtual PC, not the Windows 7 system):
1. uninstall Precision Scan LT from the XP Start menu on the virtual PC
2. delete scanner from XP Device Manager
3. detach power and data cables
4. reboot XP
5. reinstall Precision Scan LT (sj650en.exe) into XP
6. reattach power and data cables and reattach in virtual PC USB menu
7. click to confirm unsigned driver install
8. click to confirm reboot
9. after reboot, reattach in virtual PC USB menu
2) extract files to any folder (with any file archiver), for example with 7zip
3) than select the file "DPInst64" (for 64 bit windows 7/8) or "DPInst32" (for 32 bit windows 7/8)
4) choose "propreties"
5) than select "Compatibility mode"
6) choose "Launch in compatibility mode"
7) select "Windows Vista (Service Pack 2)"
8) click "Apply", than "OK"
9) right click on file that you modified and choose "Run as administrator"
10) If it shows some preventions click "OK"
11) Ignore any preventions about wrong installation (if it appears in the end)
Now it should work!) Try to use your scanner!!!