I'm going to necro this just once. Seeing a lot of people in this thread struggling to get these working.
Well, I just got one, new in box, with a driver diskette (see below). It's got Belkin branding on the top of it (but doesn't in the picture on the box). It looks near identical to all of yours, and exactly identical to Pierre32's except for a different FCC ID.
It has FCC ID of IOWCM-PS2C (instead of IOWCM-290F), which has the same "IOWCM" prefix as the rest in this thread - i'd guess the "PS2C" is because it can also work in PS/2 mode if it detects being plugged into a PS/2 port. Serial is done via a pass-through adapter. That doesn't change the other serial protocols that it can communicate over; it's effectively trilingual, and the other two modes (selected via the switch on the bottom) are identical to all of yours.
It came with a floppy disk, which I was able to make an image of.
The "PC AT" side of the switch puts it into "Mouse Systems" protocol. Mine works (moving and clicking) on my PC using 'inputattach -msc /dev/ttyS0' on my linux system in that mode, with all three buttons. Inputattach (and gpm) are basically linux/unix equivalents of what cutemouse does in DOS.
The other side (MS AM) puts it into the Microsoft two button mouse mode; in that mode, Windows 98 detects it as a non-plug-n-play device when I make it search for non-PnP devices in the device manager, and then configures it for me. No external drivers needed for that mode.
...But I have another mouse that has the exact problem OP's had, where it can click just fine, but can't move. That one used to work, and then stopped one day! - so I think probably we're looking at hardware failure, not a driver issue.
Furthermore, when I point my phone camera at the optical gates on the new mouse and run 'inputattach,' the LED's light up (in infrared, so only visible on my camera). But they do NOT light up on the other mouse! - so I'd hazard a guess that the LED's are either dead, or some other piece of the electronics that drive the LED's is dead. Maybe you could try doing this on yours and see what you get.
Edit:
Well, I tried to redo the experiment taking pictures with the camera, and lo and behold now both are powering up and working. I wonder what the heck I did... Maybe wave a rubber chicken over yours, or press down on some of the components on the PCB. Weird.
Anyway, might be worth checking if your IR LED's are lighting up. They WEREN'T for me (but are now).
Edit again:
It stopped again. But, with a camera aimed at it, i figured out that by pressing down on the cable where it meets the DE9 connector i can make the led's light up again. Clicks always work regardless. So it's clearly a problem with my cable in this mouse. I'd suggest you try replacing your mouse's cord or the DE9 connector at the end of it.
Oh, and have the driver diskette. DOS, Windows 3.1, and Win95 drivers. In case any of you actually do need them. I haven't tried this new one in Windows pre-NT yet, so maybe you do. But I kind of doubt it. I've heard you can make cutemouse work within the DOS-based versions of Windows.
https://archive.org/details/belkin-mouse-3-bu … al-mouse-floppy
P.S. - I have yet to find a Win2K/XP (or NT) Mouse Systems 3 button serial mouse driver. There was one on Mouse Systems' website around 2000, but that's long gone and the file itself is missing on archive.org. So for those OSes you may be stuck in 2-button Microsoft mode unless you're more clever than I am and manage to find a driver somewhere. I'm personally enamored with the IBM ScrollPoint mouses for WinNT, so I can cope without the serial mouse there. But these serial ones (or one of mine, at least) can also talk PS/2.