Well, this is going to sound like one of those walk 2 miles uphill to school stories, but what you are trying to should be possible.
The 'optimal' solution on a non-PCMCIA laptop is a Xircom Parallel Network adapter. That plus the MS Network client (in the clients directory on any NTS CD) plus some tweaking should get the DOS machine talking to NT.
If you only need to transfer a few files, it would probably be easier to get a Null Modem cable between the serial ports. Use any DOS Comm program and HyperTerminal and then use Kermit, XModem, YModem, or ZModem (best) to transfer the files.