Unfortunately, detailed instructions are not likely to be forthcoming. Troubleshooting network connections typically involves a lot of experiment and observation (much of which you have probably been through with Drew).
Getting the router and straight cables was a big step forward. It will give you additional diagnostic tools, and will also allow you to introduce a third computer as a tiebreaker if you need to (i.e. if A can't connect to B, then see if A can connect to C, or if C can connect to B).
My guess is that the provided Linux kernel does not contain a suitable driver for your 3COM network card. You may find some useful information in the dmesg.txt file, which is among the files generated when you do F7/Utility, F7/Report. Look through it for a block of messages that talk about "eth0". Post back here with a copy of all that you find there. For example, here are the messages from a system that I am pretty sure correctly connects to a network:
Code:
0 3c515 cards found.
cs89x0:cs89x0_probe(0x0)
PP_addr=0xffff
eth0: incorrect signature 0xffff
PP_addr=0xffff
eth0: incorrect signature 0xffff
PP_addr=0xffff
eth0: incorrect signature 0xffff
PP_addr=0xffff
eth0: incorrect signature 0xffff
PP_addr=0xffff
eth0: incorrect signature 0xffff
PP_addr=0xffff
eth0: incorrect signature 0xffff
PP_addr=0xffff
eth0: incorrect signature 0xffff
PP_addr=0xffff
eth0: incorrect signature 0xffff
PP_addr=0xffff
eth0: incorrect signature 0xffff
PP_addr=0xffff
eth0: incorrect signature 0xffff
PP_addr=0xffff
eth0: incorrect signature 0xffff
PP_addr=0xffff
eth0: incorrect signature 0xffff
cs89x0: no cs8900 or cs8920 detected. Be sure to disable PnP with SETUP
8139too Fast Ethernet driver 0.9.18a
PCI: Found IRQ 11 for device 00:0e.0
PCI: Sharing IRQ 11 with 00:07.2
PCI: Sharing IRQ 11 with 00:07.3
eth0: RealTek RTL8139 Fast Ethernet at 0xc4000000, 00:0c:76:59:7f:c0, IRQ 11
It is experimentally probing for various known network card types. It checked for cards with the 3c515 chipset and didn't find any. It checked cards with the cs8900 chipset, and didn't find any. That check wasn't very graceful, and generated all the "incorrect signature" messages that look alarming but don't mean anything. Then it checked for a card with the Realtek RTL8139 chipset; found one; noted that it is sharing an IRQ (which is probably okay); and started up the driver.
Show us what you find in that part of your dmesg.txt. Also look for a section that mentions dhcp, zcip, and/or "promisuous mode". That is probably after "freeing unused kernel memory" and before various "usb.c" items.
Also let us know what you have in cnc10.net (with password x'd out if you prefer).
What do you get when you enter the command ifconfig at a Linux command prompt?
If it turns out that the kernel does not have a driver that recognizes your card, it will probably be easier just to find a cheap RTL8139 card to use instead.