When you got the new pc, are they both running the same os? was old one an HP whilst the new one is something else?
To tell the truth, this sounds like a printer driver issue, you might try uninstall and reinstall of it, and if that doesn't work, might download new driver for it. My epson won't work in windows 98 without doing some crazy stuff and printing fuzzy like, but in Windows NT, it prints fine. Haven't tried 2000 or win Me.