My cable is plugged into the slot next to the USB ports in area4, and it is lit up with a green light that occasionally flashes orange.
I cannot speak from personal experience on this specific machine, but if there are TWO lights on the network port, the orange/amber LED normally indicates speed and should not alternate - while the second LED normally indicates activity/traffic/etc. If there's only ONE light, it's possible this alternating colors was intentional. I'll do a little digging to see if I can find a determination, but just for sake of trying, if you have another Ethernet cable I would swap this one out and see if there's a difference.
UPDATE: According to the owner's manual, there are two LED lights. On the RIGHT side of the cable should be a SOLID GREEN LED which indicates a solid connection to the network. On the LEFT side of the cable should be an amber (orange) LED which flashes according to activity on the network. This LED should not alternate colors.
Click Here for the owner's manual
I have an extra card in the area 5, which I think is a graphics card. It has nothing connected to it.
If you're willing and able, unplug the machine and remove any unused cards from the system to free up Interrupt channels.
Also, in BIOS, disable COM/Serial ports, floppy drives/controllers... anything you do not NEED to fire up the machine with.
There are multiple Inspiron 530 models, some had ATI video cards, Sound Blaster cards and/or Telco Modems installed at the factory.
Next, go into BIOS and see what VERSION of BIOS is installed. Their most recent (2009) is v1.0.18
On the Dell website, there's also mention of a RealTek 81xxxx driver which based on the driver information I'm going to speculate it was their "fix" as the Intel chip caused quite a bit of grief back in those days. If the RealTek was a plug-in card, which it probably was, this won't involve us.
Finally, I need to know what version of Tiny Core you are using for this adventure.
You noted you have WinXP running on it - does Ethernet work under Windows?