Ok, here's what I would suggest (as a former HP printer support tech):
1. Make sure that you have a direct connection between the printer and the computer, no data switches or zip drives or any other devices on the LPT port.
2. Try to find a "known-good" cable, one that a friend is successfully using for example, and test with a DOS print test. This is done by exiting from Windows to MS-DOS mode and using the command
dir>lpt1
It is possible that all the problems reside in the cabling.If this test fails with a "known-good" cable, then perhaps the friend might allow you to test the printer from their computer so that we have a "known-good" printer port on the computer and a "known-good" cable which could then point us to the printer or the computer port itself as a source of the problem. Once you have a successful print using the "dir>lpt1" test, you can proceed with testing in Windows.
3. In the printer properties under Start>Settings>Printers go to the "Details" tab, hit the "Spool Settings" button and "Disable Bi-directional printing to this printer". Set the "Spool Data Format" to "RAW", and click "OK". Back on the Details tab, hit the "Port Settings" button and deselect both choices there. Apply the changes.
3. Make a test document in Wordpad and print it several times. You can make this document by copying and pasting text from some other document if you wish. The purpose of this test is to determine whether the printer driver is functioning properly in Windows, rather than testing from some other application that adds another layer to the software puzzle.
If this is successful, but problems persist when printing from other applications, then the issue would be with those other applications and I would seek a solution at their vendors' websites.
Hope this helps.