Yup, you're on the right track. Here's where you're at plus a little lingo.
I've got the exact same NIC (network interface card) a.k.a. network adapter. Hell, a whole damn lot of PC's I work with have that RealTek chipset.
Next, the cable: good to go. CAT5 (re: Category 5E) crossover cable.
Not sure what you mean by "LAN card ... that is connected to a switch linked to my ISP". Please elaborate. I'm imagining you've got one NIC in your PC, and that's connected via a network cable (a STRAIGHT cable) to a DSL or cable modem of some sort (re: your ISP). What's the deal with the switching?
Are you planning then to install a second NIC into your PC specifically to hook the XBOX up to (re: two network adapters in your PC case, one going to your DSL/cable modem and the other to the XBOX)? Really, please tell us more about the switching thing. I'm just having a hard time understanding.
You see, what most people who have just the standard one NIC in their PC do is to buy a hub or a router (damn near the same thing). Like me, I bought a $20 network hub, which has one "in" port and any number of "out" ports (four is common, although eight or more port hubs/routers exist). You take the cable coming out of the DSL/cable modem and plug it into the "in" port of the hub/router, then plug the cable coming from your PC network adapter into a free "out" port. You also run a STRAIGHT cable from your XBOX to another free "out" port on the hub/router.
The hub/router moves around all the data from where ever it comes from to where ever it needs to go. What this setup achieves is:
1) Your PC and XBOX are connected, allowing for PC <--> box FTPing
2) Keep your PC connected to the internet (your ISP) allowing you to use your computer on the internet normally, without having to install a second NIC.
3) Connects your XBOX to the internet as well, enabling you to use the REALLY cool features of apps like Xbox Media Center (watching movie trailers, listening to web radio, playing online with certain games (without XBOX LIVE) by using a PC program called Xlink), and the auto-update features of certain programs.
So, that's the story. Tell me more about want you want to do and we'll see what needs to be done. Honestly, I suggest the hub setup, as it allows you to connect another PC, XBOX or whatever easily. Feel free to PM me, not with lengthy messages, but just to let me know you've posted a reply. I'm all over these forums and may not notice and reply. Let's keep the discussion here so others can offer advice.
One final question: Do you plan to install the ICE yourself? Because, no offense, if so, and these kinds of questions need answering, you may want to think about how much more complicated a mod install is (even if you take the slacker way out and go solderless).