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Out of curiosity, why are you using 162.10.10.1 and 162.10.10.2? The 162.10.0.0 block of addresses is a valid set of internet addresses. What you want to use is a non-routeable IP block such as 192.168.0.0 (or 172.16.0.0 or 10.0.0.0), so you don't cause lots of confusion if you attach your computers to the internet.
If you have a crossover cable running between the two machines and you see each other in network neighborhood, make sure that any firewalls are off (for the moment, at least). From there, check and see if one computer can ping the other. This should be the most basic test - if this fails, chances are everything more complicated will fail as well. If you can get this working, test file sharing (you'll need to authenticate using an admin account on the other computer) and so on.
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