I really have no idea how this happened, I've been running mIRC on win7 for a couple of weeks now on this laptop-I ran it for months on an old thinkpad t43 without any issues. Not sure how to reproduce it, if I do figure out what's causing it I'll be sure to update.
mIRC doesn't control what it looks like in the taskbar, Windows does, so this is likely not mIRC's fault. Remove it and add it back, and it will probably show up again.
I had no trouble with mIRC's icon in my task bar. By the looks of it, that is the default icon for a shortcut that cannot find its host file. As the other poster suggested, just delete and re-add.