do they both open and quickly close or just one does that? you could rename one, both the exe and the directory name (and of course the path on the desktop icon for it). i have multiple copies/versions of mIRC all over the place, but each directory has a diff name, like mIRC615 or mIRCtesting, etc.
As said, there could have been an install glitch, its important to close any mIRC (and any other apps too) that you have running before installing a new mIRC.

Wouldnt hurt to run 2 or 3 good virus scans to be on the safe side.