Ok when you click "System --> Administration --> Printing (Cups)" is the
proper printer installed in this dialog box?
If it matches the model now check the printer by right clicking and
choosing "Properties".
In the box that says Make and Model is there an hpijs in the description?
You can always do a new printer setup of that printer by clicking on the
"New" dialog in the Printing Configuration.

Most people call it Cups because that is what the underlying software
that runs the printing is called.
If you got it to print with the live CD(DVD) then it most likely is not
the printer or the cable.. I have had the same problem with 8.10 and 9.04.
Until 9.10 came out I had to stick with 8.04 because of my HP Laserjet
printer which is parallel and it would work fine with the Live CD then
balk after full install.

Within Ubuntu installing most hardware is similar to Windows you just
have to think outside the box and forget what you remember of Windows.

Lastly did you upgrade from 9.04 to 9.10 or did you do a full install of
9.10?