can you post the output of lspci

Install pcmciautils.tazpkg

modprobe pcmcia

With ethernet adapter plugged in use pccardctl status , pccardctl ident,
pccardctl info ,pccardctl eject ,pccardctl insert commands.
Give us whatever info you can from above commands or applicable errors from /var/log/messages

Hi,

this is terrific, thanks a lot in advance for your help. pcmciautils was already installed, and I executed the modprobe command again. Below you find the information I collected:

lspci:
00:00.0 Host bridge: Intel Corporation 440BX/ZX/DX - 82443BX/ZX/DX Host bridge (AGP disabled) (rev 03)
00:04.0 VGA compatible controller: Neomagic Corporation NM2200 [MagicGraph 256AV] (rev 12)
00:05.0 Bridge: Intel Corporation 82371AB/EB/MB PIIX4 ISA (rev 02)
00:05.1 IDE interface: Intel Corporation 82371AB/EB/MB PIIX4 IDE (rev 01)
00:05.2 USB Controller: Intel Corporation 82371AB/EB/MB PIIX4 USB (rev 01)
00:05.3 Bridge: Intel Corporation 82371AB/EB/MB PIIX4 ACPI (rev 02)
00:09.0 Communication controller: Toshiba America Info Systems FIR Port Type-O (rev 23)
00:0b.0 CardBus bridge: Toshiba America Info Systems ToPIC97 (rev 05)
00:0b.1 CardBus bridge: Toshiba America Info Systems ToPIC97 (rev 05)

pccardctl:
status:
Socket 0:
  no card
Socket 1:
  5.0V 16-bit PC Card
  Subdevice 0 (function 0) [unbound]

ident:
Socket 0:
  no product info available
Socket 1:
  product info: "3Com", "Megahertz 574B", "B", "001"
  manfid: 0x0101, 0x0574
  function: 6 (network)

eject:
No output

insert:
No output

/var/log/messages | grep pcmcia:
Sep 26 19:15:10 (none) user.info kernel: pcmcia_socket pcmcia_socket0: cs: IO port probe 0x100-0x3af: excluding 0x220-0x22f 0x2f8-0x2ff 0x330-0x337 0x378-0x37f 0x388-0x38f
Sep 26 19:15:10 (none) user.info kernel: pcmcia_socket pcmcia_socket0: cs: IO port probe 0x3e0-0x4ff: clean.
Sep 26 19:15:10 (none) user.info kernel: pcmcia_socket pcmcia_socket1: cs: IO port probe 0x100-0x3af: excluding 0x220-0x22f 0x2f8-0x2ff 0x330-0x337 0x378-0x37f 0x388-0x38f
Sep 26 19:15:10 (none) user.info kernel: pcmcia_socket pcmcia_socket0: cs: IO port probe 0x820-0x8ff: clean.
Sep 26 19:15:10 (none) user.info kernel: pcmcia_socket pcmcia_socket0: cs: IO port probe 0xc00-0xcf7: clean.
Sep 26 19:15:10 (none) user.info kernel: pcmcia_socket pcmcia_socket0: cs: IO port probe 0xa00-0xaff: clean.
Sep 26 19:15:10 (none) user.info kernel: pcmcia_socket pcmcia_socket1: cs: IO port probe 0x3e0-0x4ff: clean.
Sep 26 19:15:10 (none) user.info kernel: pcmcia_socket pcmcia_socket1: cs: IO port probe 0x820-0x8ff: clean.
Sep 26 19:15:10 (none) user.info kernel: pcmcia_socket pcmcia_socket1: cs: IO port probe 0xc00-0xcf7: clean.
Sep 26 19:15:10 (none) user.info kernel: pcmcia_socket pcmcia_socket1: cs: IO port probe 0xa00-0xaff: clean.
Sep 26 19:15:10 (none) user.notice kernel: pcmcia_socket pcmcia_socket1: pccard: PCMCIA card inserted into slot 1
Sep 26 19:27:58 (none) user.info kernel: pcmcia_socket pcmcia_socket1: cs: memory probe 0xa0000000-0xa0ffffff: clean.
Sep 26 19:27:58 (none) user.notice kernel: pcmcia 1.0: pcmcia: registering new device pcmcia1.0
Sep 26 19:30:22 (none) user.notice kernel: pcmcia_socket pcmcia_socket1: pccard: card ejected from slot 1
Sep 26 19:30:38 (none) user.notice kernel: pcmcia_socket pcmcia_socket1: pccard: PCMCIA card inserted into slot 1
Sep 26 19:30:38 (none) user.notice kernel: pcmcia 1.0: pcmcia: registering new device pcmcia1.0

I did some research in the web in the meantime and I believe that I need to install the module 3c574_cs. Do you agree? As I am new to SliTaz-Linux I do not know how to handle this. Do I need to rebuild the kernel with the appropriate settings, or can I find the compiled module and load it using modprobe?

Yes the 3c574_cs module is correct.
I run slitaz 3.0 and modprobe -l | grep 3c574_cs returns
/lib/modules/2.6.30.6-slitaz/kernel/drivers/net/pcmcia/3c574_cs.ko.gz
#modprobe 3c574_cs
then run
ifconfig to see if adapter is installed
if so add pcmcia and 3c574_cs to /etc/rcS.conf LOAD_MODULES=
add the adapter name from ifconfig to /etc/network.conf INTERFACE=" "   ,make WIFI="no"
you may be able to connect without a reboot:
#/etc/init.d/network.sh restart

Thanks a lot mojo,

it works very well and FAST! I am absolutely fascinated about the distro, support and the fact that I can still use my old equipment: