Ok, can you verify that the cable is actually crossover? The easiest way to tell is to look at both the ends: If the colour coded wires are wired identically for both ends then it ISN'T a crossover cable - but, if the colour coded wires are wired differently for both ends then it IS a crossover cable.
If there is one thing you should know about diagnosing a computer problem it would be to always check the physical hardware and cabling first. This means you will need to verify that the network cable (and the actual network card) works properly.
It sounds to me like the cable is at fault. I would try another cable or try using the cable with a hub or switch.
Hope this helps!