Check with Software Update and HP website to make sure you have all of the updated drivers for Snow Leopard.
Repair permissions and restart your computer.
It shows up as offline, which it is not.
When you print, make sure your "wireless" printer is selected. System Preferences/Print & Fax/Print - Make sure the wireless printer is selected (highlighted) and is selected as your default printer. Two printers should show up, wireless & ethernet. On my computer, the wireless one has the #1 next two it so I can tell the difference. However, you can name your printers with any name you like. Lock the padlock. Repair permissions and restart your computer. If this does not work, you can delete the wireless printer from the side panel by clicking on the "-" sign and adding it again.
Check Apple's Knowledge Base for Snow Leopard & Lion Printer solutions and suggestions.
Printer troubleshooting for AirPort Base Stations and Time Capsule
Installing the Gutenprint and Gimp-Print for Mac OS X (10.2 and later) drivers will likely do the trick when all others fail.