Cannot add HP Deskjet 3820 printer

We have been using an HP Deskjet 3820 printer with an iMac forever with no problems. The printer is connected from the printer parallel port to the USB port on the computer using an adapter cable. Last time we tried to print the print job stopped in the middle of printing. Occasionally this would happen in the past but if I deleted the printer and then added it back everything was fine. Now, though, when I try to add the printer under the USB heading, I get a question mark, the printer name, and "driver not installed". I have tried reinstalling the software that came with the printer, and downloaded and installed the latest drivers for my system software - all with no change. HP is really no help except to tell me that a talk with a tech will cost me $30 or I can buy a new printer. The weird thing is that I can print a test page, so there is some communication between the computer and printer, but I can't actually install it to print from within an application.

Any advice would be greatly appreciated.