If everything is the same from one PC to the next, I.E. the same parallel cable, same EPIC software settings/options, EPIC, power supply, .hex file, PIC, etc, then I would suspect either a different software setting, bios parallel port configuration, or a printer driver on the desktop that's not on the laptop.

Try this, and see what happens.

On your desktop PC locate the epiccfg.ini file in the EPIC directory. Rename it old_epiccfg.ini. Copy the epiccfg.ini file from your laptop into the desktop EPIC directory.

Does it work?