Hey JDHannan, I have a similar problem!
mIRC does not appear in the "Applications" tab, has disappeared from the tray, but is still shown as a running process and is still connected to any IRC networks you may have left it connected to.
The way I usually solve this is by using a free application called "Process Explorer" by SysInternals.
http://www.microsoft.com/technet/sysinternals/utilities/processexplorer.mspxIf you find the mIRC process in this application, then Right Click and select from the menu: "Window > Bring to Front" it should make it appear again!
I don't know if there's a simpler way to to this, but good luck!
