... and DSL is, as it says "Damn Small". It doesn't have all drivers a full-blown Linux desktop-system has.
But first of all, have you tried assigning an IP:
# ifconfig eth0 192.168.1.2 (as root)
If it doesn't work, try booting with Knoppix, Ubuntu, Mepis... - most likely the card is configured. Then run 'lspci' and 'lsmod' to see what the card is called and what driver you need.
Finally google for your driver.
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