mIRC usually installs to c:\mIRC, or c:\program files\mIRC, so if it's in System32\ I think you've likely caught a virus that uses mIRC.
You can remove the startup entry by going to start menu, run, then type in "msconfig", go to the "Startup" tab, find "mIRC.exe" or similar in the list (it may not be named mIRC if it was installed by something else, so you'll need to find the process name), then untick it and click on ok/apply, then restart your computer when prompted. I would try ending the process before you do this though, as it could just make it start up again every time you try to remove it.
I would try virus scanning your computer with a couple of antiviruses and antispyware applications as if it is a virus, it may have installed more than just mIRC. If it's starting up straight after closing, it may be that there are two processes - one that appears in the tray (mIRC), and another than makes sure mIRC is always running. This will be more difficult to take care of manually, so I suggest the virus scanning option.
Out of curiosity, if it's not too private, what were you trying to download? That may give us more of a clue about why it has installed a copy of mIRC to the system32 directory.
In the meantime, don't do any online banking or log into any important/private websites.
