Well remember that mIRC is not running during the reboot.. there is absolutely no way it can be responsible for deleting the file-- this should be your #1 hint. AntiVirus programs, however, *do* run on system launches to remove bad files... hint hint #2.
As far as the desktop thing, did you have mIRC create a desktop icon? Perhaps it isn't finishing the install sequence due to permission errors, though you say you ran as Admin.
I really can't think of any reasons why the installer would fail-- it's Nullsoft's installer which is used by many other programs, so it would be weird if mIRC was the only one affected.
