There was a song that was popular on alternative rock radio station
104.1fm (no longer under the same format by the way) in CT between
April-June 1996 where the chorus lyrics were - "Alcohol [then the
guitar went 'be-neer, be-neer'] Alcohol [again,the guitar line] , you
make me want to love you then get on my knees and crawl - oh Alcohol."
These days with iTUnes and Rhapsody I've tried to find it using
"Alcohol" as the keyword under the search to no avail. great rock
song, still remember it, still don't have it. What is the name of the
song and the name of the artist?

You wouldn't happen to be thinking about the Barenaked Ladies song
"Alcohol" (from their 1998 album 'Stunt') would you?

http://www.lyricsdomain.com/2/barenaked_ladies/alcohol.html

Is it Butthole Surfers off "Idependent Worm Saloon"? They have a song
called "Alcohol" on that album.

no. I just listened to both the Butthole Surfers song and the
Barenaked Ladies songs but those are not it. The song I'm thinking of
is kind of harder edged than the BNL but not quite as punk as the
Butthole Surfers. Plus it's a little more British sounding.

For some reason the way you described the song made me think about
Alcohol by the Kinks:
<i>Oh demon alcohol,
Sad memories I cannot recall,
Who thought I would say,
Damn it all and blow it all,
Oh demon alcohol,
Memories I cannot recall,
Who thought I would fall a slave to demon alcohol.
Sad memories I cannot recall,
Who thought I would fall a slave to demon alcohol.</i>

I know that the lyrics of this song don't quite match the line that
you quoted but the overoll theme and the fact that you mentioned the
British sounding makes me think about the Kinks. Their <i>Alcohol</i>
song is very memorable. I was a big fan of the Kinks in the past and
really loved this song. I probably still do. <a
href="http://kinks.it.rit.edu/cgi-bin/MusicSearch.cgi?song=regular/muswell/song-alcohol">Here's
the full text.</a>

I know. I heard that Kinks tune yesterday when I went through all 107
songs with Alcohol in the title on Rhapsody Music Service by Real
Player. Close. The song that I'm thinking of has a newer British rock
sound.

Did you ever find out what song this was?  I too have been trying to
find this song and doing it in many of the ways you have mentioned.  I
just can't believe it is this hard to ID!
Anyway, if you've found it, please let me know.
regards,
Chris.