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