a crossover cable can connect a computer to a computer w\o a router.
most cables you buy are straight through unless they say there crossover, your 360 should have came with a cable that is white and crossover
here is the actual difference
also, connecting your 360 via dial up isnt possible i dont think. even if it is you wont be able to play online, your ping will be too high, and 360's tend to use a lot bandwidth than a regular pc. you will be able to see news and stuff but not much else.