This is what the MS DOS Command -verbose told me...
Microsoft Windows XP [Version 5.1.2600]
You're not using DOS, you're using MS WinXP command line.
Huge difference.
(DirectX, Direct3d, DirectDraw, DirectInput, RawInput, etc are windows only.) [rant=off]

error: trailing garbage: "1" on line: 86 of file: mame.ini
ignoring line
What's on line 86? Probably not the problem, but should be checked out anyway.
Using RAWMOUSE for Mouse input
Mouse 1 : PS/2 Compatible Mouse
Mouse 2 : USB Device
Mouse 3 : Elo Serial Touchmonitor Interface
Mouse 4 : HID-compliant mouse
...
Serial Elo Touchscreen
PS/2 Mouse
PS/2 Keyboard
USB Thrustmaster 360 Modena Steering Wheel and pedals
USB LCD Topgun
Windows is showing mame 4 mouse devices, you only list three. I wonder what the fourth mouse is? (Not important, though.)
### Input device options ###
mouse 0
joystick 0
lightgun 1
dual_lightgun 0
offscreen_reload 1
...
lightgun_device mouse
Okay, just FYI, this setup is like having "mouse 1" for all games that mame thinks used lightguns. Some people on some versions of mame do better with mouse disabled, others with it enabled. After you try the next paragraph and if still doesn't work, try disabling by changing the last line to say keyboard just like the others above it.
Finally get to the help.

IIRC, that version of mame is forcing multiple mouse support. Your gun isn't mouse 1, and only mouse 1 is mapped to player 1. Just like joystick 2, mouse 2 is mapped to player 2, same with 3 & 4. So you need to remap the gun (mouse 2 or 4, not sure with what's shown) to player 1. Start game, tab, "Input (this game)" (<-- I'm assuming you want to use you mouse for other games), go to the lightgun inputs, err... just
follow this wiki. You
might have to disable mouse to remap correctly (mame should show lightgun, not mouse, as remap). You can repeat this for all lightgun games you want to play, or apply to general and effect all games by doing it to "Input (general)" instead of "this game", or make ctrlr files (IIRC, done differently than current mame).