Ask Slashdot: Old PC File Transfer Problem

An anonymous reader writes I have an old Compaq Contura Aero laptop from the nineties (20 Mhz, 12 Mb RAM, Windows 3.11, 16-bit, PCMCIA, COM, LPT, floppy) with 160 Mb drive that I would want to copy in full to a newer machine. The floppies are so unreliable — between Aero's PCMCIA floppy drive and USB floppy disk drive — that it is a total nightmare to try and do it; it just doesn't work. If that option is excluded, what else can I do? I have another old laptop with Windows XP (32-bit, PCMCIA, COM, LPT) that could be used; all other machines are too new and lack ports. Will be grateful for any ideas.