I'd love the opportunity to assist you. Please follow these steps:
1) If your device is connected via USB, disconnect it.2) Go into the Print & Fax system preference, right click on the printer list, and select "Reset printing system..."3) Open /Applications/Hewlett-Packard/HP Uninataller.app and when you get to the Uninstall screen (the one where the button says uninstall) press and hold Shift-Control-Command-Option while you press the button. Say yes to the scary waring message.4) Install version 2.2 of the Leopard Print driver bundle from Apple.com.This should give you Print and Scan (through the In-OS Scan Drivers). If you want to install HP Scan, then:5) Install the full solution for the Photosmart C4680 from here.Know that HP Scan Pro and HP Message Center are not compatible with Snow Leopard. But Snow Leopard does contain a full feature Utility (HP Utility) for your device.
No worries. I'll be here tomorrow and open to assist you in case we have to try another set of steps.