Any errors on the printer control panel, event logs or screenshots you can share with more information about these errors?
At the moment it sounds more like a driver issue since driver problems typcially allow a document to print up until a certain point. The most common problem is a PCL.XL problem which is prevented by migrating to a Post Script UPD. You mentioned trying PCL5 which should not have PCL.XL errors so perhaps it is some other more generic PCL problem.
Another good test would be to fire off the reports on the printer and see if you can get more than one page to print. There should be a variety to choose from on the 1312. Configuration reports are normally multiple pages. If you can get reports to print, and printing from XP is fine then there is a stronger case for a driver conflict.
Might be a good idea to download and install the latest Universal Print Driver for Post Script from HPs site. See if you can have any influence on the problem and make sure you are installing the correct version for your 32bit Win7.