The link was to specs for: M51GM-S2G GeForce 6100
But you restate that you have: M51GM-S2G GeForce 6100
Perhaps you can find a link to your board which shows your network card?
There is another possibility, in that the forcedeth driver packaged with DSL3.3 does not support your forcedeth card.
I am guessing the card works in puppy and fedora? I see from the dmesg output that the forcedeth driver is being bound to the card - so this would be a pretty good indication that this is a forcedeth compatible card all right.
I am also guessing that the forcedeth driver used with DSL is the one that comes with DSL?
So - what I would normally suggest is editing /etc/modprobe.conf and adding:
alias eth0 forcedeth
I tad trickier for a live distro.
I think you should try DSL-n
http://www.damnsmalllinux.org/dsl-n/
This uses the 2.6 kernel (like puppy and fedora) and there are reports of DSL-n working where DSL dosn't.