The following AppleScript does what you want:
tell application "Finder"
make new Finder window
Open Script Editor in the
/Applications/AppleScript folder, and paste the above in to a new script. Save it somewhere as a "File Format: Application" with "Stay Open" not checked.
Then drag that application to your Dock. When you click it, the Finder will be brought to the front and with a new finder window.
The disadvantage is, this takes about 1.5 - 2 seconds to run on my machine. I could probably tweak it by making the script stay open and watch for being brought to the front... You might also get better performance by saving it as a normal script in your "Scripts" folder and putting it in the scripts menu.