Don't suggest a wireless router, they do not work in my house, I have tried 3 different brands, each one good, and they don't work (too much steel supporting between my study and my bedroom)
Suggestion:
Yes, you can connect to xbox live using that setup.
The easiest and most common setups are as follows:
If you only need one of your devices online at any given time (360 or Laptop), then the simplest and cheapest option is to unplug and replug your devices whenever you need to.
Pros: Cheapest, only needs 1 CAT5 cable
Cons: If you switch a lot, it becomes irritating and time consuming, and you risk damaging cables if you're a klutz/impatient
If you want them both connected, don't mind losing a small (very small) amount of connection speed, and your laptop has 2 ethernet ports then you can use the laptop as a mini-router, and bridge the connection to the 360 through the laptop, (this isn't too difficult to set up in windows vista, i have no experience on other platforms though).
Pros: Fairly cheap, only needs 2 cables
allows both devices to connect at once
Cons: Laptop will slow the connection slightly before it gets to the xbox (probably not noticed unless you play *really* high-demand games
The last (and priciest) option is to buy a router or a switch, and connect the two devices to the router.
Pros: Better connection quality/speed
both devices connected at once
Cons: Expensive (a high speed router can be AUD$200+)
messy (you need to have 3 cables and a router all connected)
so there's your main options, there are others, such as Powerline or installing twin ports but they are harder to find and/or setup
