Not all USB mice can use such adapters. The mouse has to have the circuits to support PS2 as the adapter you noted rarely has more than wires.
Bob
I'm trying to get a USB mouse to work with a PS/2 to USB adapter, since my USB ports all fail to work, but it wont stay on. My PS/2 mouse is dead so I've bought a cheap PS/2 to USB adapter off of Amazon and plugged my USB mouse into it. Upon system boot, the mouse will turn on and then turn off after about two seconds. There's nothing I can do to turn it back on and it's being to get me annoyed.
I know the mouse works fine since I just tried it on a netbook and it worked upon plug in. Does anyone have advice to offer?

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