A while ago, my wheel-button stopped working randomly. After some while, it stopped working completely, so I repaired it (and made it indestructible).
What you will need to repair it yourself:
To access the screws of the G602, you will need to remove the gliding pads. Be careful when doing this and get completely under the glue-pad to prevent seperating it from the gliding pad.
Now you will be able to see the screws. Remove them.
After you opened the mouse, you will see a white pushbutton. Apply a bit of solder to the legs to improve thermal conductance and desolder the button. Alternatively, you can cut the leads and desolder them invidiually.
Now you can solder in the new button. I used an SMD button because I had them laying around. I suggest using SMD buttons because you can just bend the leads under the case and solder it without having to empty the solderpad holes. The orientation of the button is crucial since two leads are always shorted together. Just keep it the same orientation as on the old button.
Just put the case halves together and screw the phillips screws in.
Ta-da! Your mouse-wheel button works again!