Ok, I recently moved into an off-campus apartment with an ethernet
link all ready to go. I was told that I could use my Linksys BEFSR41
wired router to share this connection with my other pc (before I moved
in). Now that I am here, and trying to set everything up, I am having
problems.

I have the cables right.. ethernet cable to the WAN port on the
router, separate cables from 1 and 2 slots on the router to the pcs..
and in network connections on the pcs, I am getting LAN connected. On
the host pc, I also have a Internet Connection gateway above the LAN
connection.. it says "Disabled". I tried right clicking it and
selecting Enable, and it tells me that it is connected but it still
reads Disabled. And of course, neither pc can access the internet.

I have asked the apartment manager to give me information about the
provider and he told me this: DSL is provided by Speakeasy. Ethernet
is provided by the apartments. We do not support routers, only direct
links.

I feel as though I am getting the brush off from them and am unlikely
to get any further, useful information. That's why I have turned to
the community here to help me get this resolved.

Other facts:

Ethernet link is working, as when I have just a direct connection
without the router, I can get one pc on the internet.
Both pcs are running Windows XP Home.
Both pcs set to obtain IP automatically; router has DHCP enabled. 
Both pcs are part of the same workgroup.
I don't have a modem for this connection. The ethernet cable runs from
the ethernet outlet directly to my external router.
I'm not trying to share files with both pcs, I just want them both to
share the ethernet connection.