When you click on 'Start' you should see two columns. 'Devices and Printers' should be in the right hand column. Clicking on that should show things like you monitor, mouse, etc. In the 'Printers and Faxes' section you should see an icon for your printer, with a white tick on a green background next to it (to indicate that it's set as your default printer).
If the printer's not even shown, you need to reinstall the driver for it. (instructions on request). If the printer's shown, but there's no green tick, right-click on the icon and select 'Set as Default Printer'.
If the icon and the tick are both there, right-click on the icon and select 'Troubleshoot'.
If that doesn't sort things out, click on the link here to download HP's diagnostic software. Save it to somewhere convenient on your computer, then double-click on the downloaded file to run it:
http://whp-hou9.cold.extweb.hp.com/pub/printers/hppsdr/HPPSdr.exe