Amiga Explorer should be completely independent of your network card. No idea why it's not working.
Samba is probably a better method as it uses your existing network connection (and will be much faster than a serial transfer). Version 2.0.7 is the most stable and functional 68K port. See
http://www.amigasamba.orgAn alternative installation guide is available at
http://samba.amigaworld.net
