Are you using Hewlet Packard's printer driver software, or generic printer drivers included with your operating system?
Last time I had a problem like this, there were two different programs causing a conflict on the computer. The paper size and settings in both programs had to be exactly identical or everything would lock up. Since 99% of printing was straight to A4, this problem only appeared when trying to print photos on 7x5 photo paper.
The most satisfactory solution was to disable the Microsoft Windows generic print driver and use the HP drivers exclusively.
Check in your control panel, printer settings, and disable Windows drivers, leaving the HP ones enabled. Consider disabling and/or deleting all printer drivers for your printer. Then download the latest drivers for your printer from HP and reinstall them. That should at least resolve any possible conflicts.