First you have to narrow down the variables involved. First, never trust what you see in Network neighborhood. whe way MS browser services work can be a tricky thing to pin down. And if you you have NetBEUI running you may be resolving machine names that way. PING is strictly a TCP/IP utility and will definately establish Internet connectivity.
Now, when you ping "yourself" 198.168.1.2, you are only testing the protocol stack the same as pinging the loopback address 127.0.0.1, and this doesn't tell you if you are hitting much else.
What subnet masks are you using? Probably 255.255.255.0, make sure that the first 3 octets are the same on both machine, ie. 198.168.1.whatever.
When you ping the other machine, look at the hub and NIC(eth card) and see if the green lights blip with the PINGs.
If not, then you have
A. No lights on any device,(a problem with the pinging nic)
B. No lights on the hub, (bad connection, Xover cable?)
C. No lights on the recieving NIC(bad connection again)
Even if the cards are improperly configured they should blink with the broadcast of the packets.
If they all blink like they should, then you have a config problem probably having to do with the network addressing.
Go back and read your destructions very carefully.
Hope this helps,
Troy