This is probably a remarked Lexmark Z22 printer.
Usually, Compaqs are relabeled Lexmarks. So you should try drivers for Lexmarks with the same maximum resolution as your Compaq. Either free drivers as listed on openprinting.org or drivers provided on http://www.lexmark.com/ for various models.
If at all possible, use free drivers. The lexmark drivers cause a great deal of problems, and do not work with free software like CUPS.