IT IS NOW WORKING!!!!!   

It seems like I performed the same steps as before but this time it works.  Seems like there is an order which must be followed in order to get it working, however, I did not test each different scenario out.
Here is the order which I performed the setup and after this it worked:
- Create the "C:\Mame32\ini" directory (if required)
- Delete the "C:\Mame32\ini\MAME32.ini" file (if existing)
- Delete the "C:\Mame32\MAME32ui.ini" file (if existing)
- Unzip "noname-0.81.09-mame32xp.zip" into "C:\Mame32\" directory
- Open a command prompt and go into the "C:\Mame32\" directory and perform the "noname32xp -cc" command manually.  This created the "noname32xp.ini" file
- Edit the "noname32xp.ini" file and set the following Analog Plus 
options:
    ### Analog+ options ###
    singlemouse             0
    switchablemice          1
    switchmiceaxes          1
    splitmouseaxes          1
    resetmouseaxes          0
    lightgun2a              0
    lightgun2b              0
    multimouse_winxp        1
- Move the "noname32xp.ini" file into the "C:\Mame32\ini" directory
- Double-click on the "noname32xp.exe" file to start the application.  This should create the "C:\Mame32\MAME32ui.ini" file
- Go into the "Options/Default Game Options/Controllers" and check "Enable Mouse Input" and "Enable Lightgun Input".   Go into the "Options/Default Game Options/Miscellaneous" and uncheck "Use additional Game artwork".  Click OK button.  This will create the "C:\Mame32\ini\MAME32.ini" file
- Go into the "Options/Interface Options" and set "Skip Disclaimer" and set "Skip Game Info", click OK button
- Start up a dual mouse game (ie: Pong, Warlords, etc..) and click TAB and then go into "Mouse Axes" menu.
NOTE: For some reason, the settings which are made inside the MOUSE AXES menu section are not saved after exitting the game and returning.   As a result, I need to reset the mice everytime I want to go into a new dual mouse game.  I can live with this, but it would nice to know if other people have this trouble .....
Anyway, I am now happy and have actually played my wife PONG ..... Thanks for your help !!!!!!
Regards,
UncleT