I'm interested to know what you are able to ping successfully, as that may offer a big clue. I tested with my A1200 and even with the network cable unplugged I can fire up Miami DX and successfully ping the address assigned to the network card. Are you able to ping something else on your network e.g. your router or anything out on the Internet?
Continuing with the network unplugged if I then try to load up a web page in Aweb I get a blank screen but nothing indicating that anything was downloaded. Ibrowse looks like it's trying to do something and eventually gives me a DNS error.