I'm failing to connect my printer to my hp, my hp seem not to have the make of the printer on its list of printers

First try to power cycle the printer by turning it off and turning it back on. If this does not help, unplug the printer for 15-20 seconds and plug it back in. if this does not help, a HP employee recommended this for a networked printer (meaning connection is through network not directly to PC):

If you installed via network, then you need to send the 'scan to' settings to the printer to update the LCD list Depends on the hp software, follow following steps to update the 'Scan To' settings to the printer: HP Solution Center or HP Director Click Settings , and then click Scan Settings . Depending on your software version, click the option available to you: Scan to... Setup Button settings Click Scan to... Setup . Continue with the on-screen instructions to create a list of destinations for scans. Try scanning again from the printer control panel.

Other than that, the only solution that seems to work for most is to perform a factory reset. Here are the steps:

Settings/Tools/Restore Factory Default or

Setup/Tools/Restore Factory Default

This is done through the menus on the printer itself.

First check your devices and printers and see if its listed. If it is check to see if its the default printer. If it is listed make it default. If it is not listed install software from HP support under your HP C309a. With the software downloaded and saved to your computer (I would download the complete software not just the driver)you should be able to connect that printer to your computer and the rest of the network.

Did you check the Microsoft Compatability Listing for the model 630 printer? There may not be a driver for your Vista 64 OS. Search Microsoft Compatability List using your favorite search engine to find the list.

If your printer is listed, great. If not, you will have to go to www.hp.com/support to find a driver. If none is offered there, you can always ask HP. HP responds to public inquiry for drivers if there is enough interest shown. Failing that, you might find 3rd party drivers that may work to your satisfaction. ... and alas, lastly, if you can't find a driver, your alternatives are limited to: Running your printer on a compatable computer/OS, using that computer as a print server on your network or ... purchasing a new printer.

Click on Start -> All Programs -> HP -> HP Update and run this utility. Last month, HP released an update that directly addresses this issue with the PhotoSmart series printers and computers using Vista. You should install any updates listed here, including the connectivity update.

I do not know which driver you are using since three different Ones are listed  8,9, and OS-X. I f you are not using OS X  or at least 9, I would consider trying them , if I were you,since you are currently using 10. The driver page states that if you OS in not listed. then they do not recoment this printer,in so many words.
http://h10025.www1.hp.com/ewfrf/wc/softwareCategory?lc=en&dlc=en&cc=us&product=304431〈=en&

A list of HP aio error codes:

http://h10025.www1.hp.com/ewfrf/wc/document?docname=bpu02549&cc=us&dlc=en&lc=en&jumpid=reg_R1002_USEN

You could try running the Fax test. Press setup > Tool> Run Fax test.

This will give you instructions about what you need to check and what you need to do if it failed on some of the tests.

Then try to send a fax to the HP fax test server detailed below:

http://h10025.www1.hp.com/ewfrf/wc/document?docname=c00259105&cc=us&dlc=en&lc=en&jumpid=reg_R1002_USEN

Hi

Please make sure that the Drive is working.
Clean the CD with the plain cotton cloth and try once agqain.

If still it fails to work then download the driver form the Below link.
Make sure you choose the right operating system from the list for us PC/notebook

http://h10025.www1.hp.com/ewfrf/wc/softwareCategory?lc=en&dlc=en&cc=vn&lang=en&os=228&product=1128296&

i hope this will solve ur problem
Best of Luck

Set powermode "allways on" for the lap top. Use an Usb cable no longer then 2 m. Try upgrade firmware for the printer. If still got problem use a powered usb hub between laptop and printer.

Sounds as though one of the drum cleaning blades is failing.

When you see the double image shadow, is it any particular color? If so, that's the drum unit that is failing.