Hmm, well I don't know of any mIRC option (without scripting) that would make you beep when you send a message to a channel. If Sounds are disabled that's even stranger.
I suggest you download and install a clean copy of mIRC from www.mirc.com/get.html
- make sure you save it to a different directory
from your current mIRC. Make sure you choose not
to keep any old settings when it asks you. After this you should then have mIRC in a completely empty folder with no script files.
Start it up and see if it still beeps. If it does NOT then you simply must have some sort of script which is causing it to beep. By default it will beep when you connect, ignore that - I mean when you type something into a channel.
Again make sure remotes are OFF, you should see * Remote is off
echo'd into your window.