I had similar problem. Replaced batteries with well known alkaline batteries and was not able to get mouse to work or green light on when I switched mouse on.
Then replace batteries with cheaper batteries and it worked!
Not sure if mouse is very sensitive an the new alkaline were just too powerful for mouse, but cheaper (still alkaline) batteries worked! So try different brand and see if you get same result.
Hope this helps.
Some ‘dumb’ questions just so we don’t assume what you have done:
Batteries installed with both + poles pointing to the top as you hold the mouse?
Mouse switch has been returned to the ‘on’ position - do you see a green light? First it will be solid green and then flashing green as the mouse tries to pair with the computer.
Try clicking the mouse a few times as it’s trying to pair.
If you don’t see a green light, try wiping off all battery contacts and reinserting the batteries. If still no green light and the mouse switch is ‘on’, are these old rechargeable batteries that been recharged many times or are they fresh normal batteries (not rechargeable batteries)?
I have had this problem at different times. On another thread (I think under Blue Tooth?) someone noted that different makes of batteries, especially rechargeable batteries, have different shaped contacts. They had a picture of this. The differences meant that the batteries of some makes just didn't fit properly. I still have to jiggle it sometimes because the back of my magic mouse is loose and comes off. But generally its been better since I found that the Energizers seem to stay connected longer. A search on this subject might find the thread for you.
Whenever you change the batteries in an apple wireless mouse, you disconnect it from the mac that you use it with. Once you put new batteries in the mouse, you can try clicking a number of times on the mouse until the mac recognizes it again. Rarely, the mac will not connect to the mouse again and then you must connect a wired mouse and re-setup the mouse with the bluetooth menu. If the mouse does not show up in the bluetooth list anymore, replace the replaced batteries.
Am experiencing exactly this problem on my father's iMac running 10.6.8! However, I have never had any problem changing mouse batteries on my own iMac, which up to recently was running exactly the same system (I have now upgraded to Lion and still have no problem changing batteries.....) Any suggestions?!