Thing is I can ping either computer (10.0.0.1 or 10.0.0.3) from the other. But I cannot access either when I try to SSH. That is with the firewall on both computers off.
From reading that thread it seems the problem was that other computers were not even issued IP addresses on the internal network. On mine all PCs receive IP addresses and can access the internet without issue.
Go to Network Wizard. Add new connection. Choose Other at first step box.
Then choose the first choice on the next step. Follow the instructions.
Your folders must be shared for your local network users to "read" you.
You should know be able to see the rest of the network group pc's in My Network Places if the other pc's network setup was similar.