I have this same problem on my A500. It started happening shortly after I moved my computer from one desk to another and seemed to just spontaneously stop working.
Like the OP the mouse buttons work fine, but I can't move the mouse at all. I tried my mouse on another Amiga and it works there, and I tried another Amiga mouse on my Amiga and got the same result (buttons work, no motion.)
It sounds like it's a fuse that's blown on the mouse port. I haven't yet taken out my multimeter to continuity test the fuses at the port, but I disassembled the Amiga and see where there's a bank of resistors and fuses near port 0. I suspect that one of the fuses is blown and I will have to replace it with another fuse. It seems like the Littelfuse Pico II fuses are the same type. I need a 100mA replacement from what I read... these seem to run about $5-6 USD which seems a little expensive for what it is.
Has anyone had this problem on an A500 or has anyone else replaced these fuses with something else?