There is no easy/magic way to "access an old PC". If you can get online with the old computer you can email yourself a copy of the document.
If the old computer has a network port you can connect the two computers via a "crossover cable" and set-up a 2 computer network and allow security access to the old hard drive. Another option is two buy an external hard drive enclosure and remove the hard drive from the old system. You attach the drive adapter, via a USB cable, to the laptop. Since the old hard drive is ancient, in PC terms, this may not be cost effective.
Good Luck