I double checked whether or not my administrator privileges were changed the moment I received the message about not having the appropriate rights to access the file, and again when re-installing today.
Try right clicking on it and choose Run As. Select an user with admin priveledges and try it that way even if you are admin. You may also try right clicking on the EXE and choosing properties. I know CHM files can sometimes be Blocked and you have to click Unblock from the properties page (the unblock button only shows if it's blocked), and perhaps it's possible that EXEs can also be blocked the same way.
Could some one perhaps list the files that this folder would usually contain, so that I can be certain that the installation was completed in its entirety?
I realize this is may be a hassle, and ultimately have no purpose, in which case, I don't want to frustrate anyone with my problem. You have all been great thus far, and as I have said, I appreciate it.
You could try just a clean install of mIRC and test that. Beyond just testing it, you can see what files are there. Really, you can get by with only the mIRC.exe file. It will create the mIRC.ini file when you run it. Of course, if you want to have the list of servers, you'll also want the servers.ini file. It isn't needed to run or connect to networks, but if you don't connect using /server, you'll want to have it. Other than that, anything else is just extra (such as the help file (mIRC.CHM or mIRC.HLP).