Unix Newbie Needs to get files off non-networked Unix box

First off, I have very limited knowledge of Unix.  The problem I'm facing is that I need to go and retrieve some .dbf files off of a server at one of my clients offices.  The system they use is extremely old and runs Unix.  They have one "Server" which has 3 "Terminals" connected via serial ports.  The only drives on the box are a floppy drive (not enough space for my .dbf files) and a tape drive (not an option because we don't have a compatible drive at the office to read from).  The Unix box is not connected to the Office Network or the Internet in any way.

Usually in offices where the Unix box is on the network, I can just ftp into the server and get the files I need, but that is not an option here.  I need to find a way to get the .dbf files off of their server and then bring them back to my office and load them into an MS Access database.

I thought maybe there would be a way to use a USB flash drive, but the Unix box does not have USB ports (it's that old).  Is there someway to plug my laptop into one of the serial ports on the Unix box and use a "Terminal Emulator" (I believe that's how this works).

If anyone can help me out with some ideas on how to get the files off (with instructions), or can give me some detailed instructions on setting up a laptop to connect to the Unix box via serial cable, I would greatly appreciate it.

Thanks for the help.
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an ancient way to transfer files over a serial cable was uucp
But of your laptop is not old enough to have a uucp, or maybe kermit, then it may be easier to break the files into floppy size pieces.

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connect your laptop to the serial port and use a terminal program, most of them also support a "file transfer" mode also.
I guess you have some kind of M$ running on your laptop, so use hyperterm, or better terraterm or putty or kermit (if available)
Or CRT from www.vandyke.com
For file transfer program if rz/sz pair does not work install lrzsz ( transfer UUENCODED )
Mention uname -a output to make us help with instructions on getting and installing unix software.
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