After software installation, click Start All Programs HP Deskjet D1600 series Readme.
I had been there before but kept getting the "not compatible with Ubuntu.04" notice.
Thank you mr_niceguy, that got me up and running although I didn't have to sudo hp-setup at the end, that just worked!
How does HP install software and gather data?
Before software installation, insert the software CD, click Readme when the option appears onscreen.