I'd assume that you have to wait until your login is accepted before joining a channel on the restricted network
(which we're calling BLAH), and that the server sends you a notice that your login was successful.
So going by your third post:
on *:START: {
  server irc.BLAH.org 55000
  server -m irc.p2p-irc.net 6667 -i Invy -j #utorrent,#sportbit
on *:CONNECT: {
  if ($network == BLAH) {
    editbox -an /login username password
on *:SNOTICE:*response_text_here*:*:join #BLAHchan

Obviously you need to change:
  • irc.BLAH.org
  • BLAH
  • username password
  • response_text_here
  • #BLAHchan
to your values.

Copy the edited script to Windows clipboard.
Open mIRC.
Type ALT+R twice.
On the menu, choose File | New
Paste the edited script. [or paste the original and edit it here.]
On the menu, choose File | Save As...
and name the script something recognizable, e.g. MyConnects.mrc
Click OK.
To test, close and reopen mIRC.

Any problems, post back.