I just inherited an old laptop from my college's computer lab.

In my house, I have my desktop computer in my room connected with a wireless connection. I'd rather not buy a wireless card for the laptop, so is there any way y'all know about to connect a laptop to a desktop to get Internet? I have ethernet jacks in both computers that are unused at present, so it'd be ideal if I could just connect them from that.
It also has no CD drive so I won't be able to put Linux on it until I get it connected.

Any ideas would be great. Thanks.

Edit: Because it's old, I'd also like to be able to connect the laptop to the desktop via XDMCP or VNC too... in case that changes anything.