Without a schematic, you're pretty much out of luck. You have to know how it works and what is supposed to happen before you can analyze whether it is working. Basically, unless it is smoking when you power the system up, the way to test it is to look at each pin for the expected signal or state when it is in use.
Can you read a part number? If so, you can go to the manufacturer's site and look at application info to see if you can psyche out how it is being used in your circuit.
If it is socketed, replacing it would tell you if it's bad, or it may blow another good IC, depending on what caused the problem. If it is a complex part (CPU, controller, etc.) that is hard soldered to a board, and you don't have a lot of experience replacing them, I'm afraid you'll have to write it off or get some help. Since it's a mouse chip, I'm guessing that's what it is.
Beyond the science project value of trying to fix it, mice are so cheap that it isn't worth the effort to deal with it.