For future reference:
a) I believe ASO have stopped allowing access as http://ip.add.re.ss/~username/
because it bypassed cPanel's accounting mechanism and let people have free bandwidth
b) If you edit your "hosts" file (/etc/hosts on Linux, c:\Windows\System32\etc\hosts or something similar on WinXP and who knows where on Vista and 7) then you can add in mappings of IP addresses to domains. If your domain name is still propagating, but the server knows that it should be handling requests for that domain (i.e. it is already setup in cPanel) then you can add the mapping to your hosts file and all of your requests for that domain will go to that IP address.
The format of a hosts file is:
to map example.com to the (invalid) IP address 22.214.171.1246