You best bet is to get the drive hooked up to a USB to IDE adapter and copy the files.
If that doesn't work get and USB to RS232 cable and a NULL Modem Adapter and connect your two machines. Ideally you should setup Linux with pppd on the new computer. Run Trumpet Winsock on your old laptop and do a manual login and just hit ESC as soon as the terminal window shows up. Once that works install and ftp daemon on one of the two machines and a ftp client on the other side. Then just copy your files.