Git Diff with Beyond Compare

I have succeeded in getting git to start Beyond Compare 3 as a diff tool however, when I do a diff, the file I am comparing against is not being loaded. Only the latest version of the file is loaded and nothing else, so there is nothing in the right pane of Beyond Compare.

I am running git 1.6.3.1 with Cygwin with Beyond Compare 3. I have set up beyond compare as they suggest in the support part of their website with a script like such:

#!/bin/sh  
# diff is called by git with 7 parameters:  
# path old-file old-hex old-mode new-file new-hex new-mode  
"path_to_bc3_executable" "$2" "$5" | cat

Has anyone else encountered this problem and know a solution to this?

Edit:
I have followed the suggestions by VonC but I am still having exactly the same problem as before. I am kinda new to Git so perhaps I am not using the diff correctly.

For example, I am trying to see the diff on a file with a command like such:
git diff main.css

Beyond Compare will then open and only display my current main.css in the left pane, there is nothing in the right pane. I would like the see my current main.css in the left pane compared to the HEAD, basically what I have last committed.

My git-diff-wrapper.sh looks like this:

#!/bin/sh  
# diff is called by git with 7 parameters:  
# path old-file old-hex old-mode new-file new-hex new-mode  
"c:/Program Files/Beyond Compare 3/BCompare.exe" "$2" "$5" | cat

My git config looks like this for Diff:

[diff]  
external = c:/cygwin/bin/git-diff-wrapper.sh

Solution

I don't use extra wrapper .sh files. My environment is Windows XP, git 1.7.1 on cygwin, and Beyond Compare 3. Following is my .git/config file.

[diff]
    tool = bc3
[difftool]
    prompt = false
[difftool "bc3"]
    #use cygpath to transform cygwin path $LOCAL (something like /tmp/U5VvP1_abc) to windows path, because bc3 is a windows software
    cmd = \"c:/program files/beyond compare 3/bcomp.exe\" "$(cygpath -w $LOCAL)" "$REMOTE"
[merge]
    tool = bc3
[mergetool]
    prompt = false
[mergetool "bc3"]
    #trustExitCode = true
    cmd = \"c:/program files/beyond compare 3/bcomp.exe\" "$LOCAL" "$REMOTE" "$BASE" "$MERGED"

Then, I use $ git difftool to compare and $ git mergetool to merge.

About trustExitCode: For a custom merge command, specify whether the exit code of the merge command can be used to determine whether the merge was successful. If this is not set to true then the merge target file timestamp is checked and the merge assumed to have been successful if the file has been updated, otherwise the user is prompted to indicate the success of the merge.