Wireless printer will not perform without usb cable

It sounds like your printer is not in sync with your wireless router.
Try restarting your computer, then make sure you have Internet access. (Click on Explorer or Firefox, and if you get access, then you know your router is working)
If your router isn't working, unplug the router for 10 or 15 seconds, then plug it back in. Then restart your computer again. That should work.
Once you are sure your router is working, you'll need to make sure your printer is in sync with your router. Best bet is to follow the instructions that came with your printer. You might have to put in the CD that came with the printer and reload the Photosmart programs. At one point during that process, it will ask you what type of router you have, and it will make a connection to the router, allowing you to print stuff without using a USB cable.
(I had to go through this process three times, for three different laptops in my house, and - knock on wood - we've been having great success with wireless printing with our Photosmart printer.)