A G-line a global ban on the network, so you are banned from the entire network on all of its servers. A K-line is a local ban on a server, and so you can connect to another server on that network and it should let you on.
K-lines and G-lines have nothing to do with mIRC - We have no control over them, and the only person or persons that can deal with it are the staff of that particular IRC network. Check out this thread
for further information.