stick with the original plan (extra nic + crossover cable)... its cheap (<$20), fast (100Mbps), and if you setup ICS on the desktop you can use your internet connection on your laptop as well.
the other options (par, ser, usb) are pretty slow: upto 5Mbps usb, 0.7Mbps par, 0.4Mbps ser (according to the LapLink website & using their cables/software) also, that serial speed seems high to me... tried moving a couple files (~3MB each) from one of my computers to a friend's computer (w/o nic) using a serial connection and windows' direct cable connection... started it, went out to lunch, came back an hour later & it was barely into the first file still -- moving yes, but oh-so-slow! (ended up cancelling it and connecting his hard drive to my machine)
also, a broadband router (or a hub/switch) is a good solution, but is clearly more than you need right now. with only 2 machines, its hard to justify the additional expense. you can add one later if you have more machines to hook up (and then you could steal the extra nic out of the desktop to use on the new machine)
oh yeah, all the speeds up above are Mbps = megabits/sec, NOT megaBytes (MB)...
also, it makes life easier if you make your second NIC a different brand from the first, just so its easier to identify which you're working with when you're setting everything up.