As you get the logo the board itself seems functional.
Cable orientation could be wrong or you need a null modem cable (or if
you have a null modem cable in use you can try without).
You can also try the stuff at the revC validation page, and you can
try to make an image with Koen's generator
http://amethyst.openembedded.net/~koen/narcissus/
That one supports virtually all ethernet dongles, so you could see if
with a dongle it gets an IP address from your dhcp server (and if so
you should be able to ssh into the beagle.
In my opinion it is not too likely that your beagle is broken
Under linux, take an emtpy card then uncompress the img file and dd it
to the card
something like:
dd if=imagefile of=/dev/sdg bs=1M (i assumed sdg is your full card,
image file is the name of yoru uncompressed image).
after that mount the 2nd partition:
something like
mount /dev/sdg2 /mnt
and extract the tar file you got from the generator to /mnt
after doing so be sure to do the following:
umount /mnt
sync
and wait until sync returns and all write activity to the card is terminated.
Then put the card into your beagle. Booting hte first time will take a
long time (several minutes, depends also on hwat you have selected).
You'll see the angstrom logo on display.
Also when it is done you'll get a login screen.
Somewhere along the line your ethernet adaptor will also be enabled
(mine has a led that goes on) and at some point it will try to get an
ip address.
Feel free to come to #beagle on freenode if things are not clear.
BTW: have you tried your cable without null modem cable?
Also are you sure your cable is not broken?
If you are a little bit technical you can find the pinout of the
connector in the documentation and you can measure whether the pins on
the connector actually go to the right pins of the rs232 plug.
Good luck, FM