If your guitar does not switch on with the battery inside, and you're sure its charged, then you probably have inserted the battery facing the wrong inwards instead of outwards. I also made the mistake of thinking this battery was incompatible as well, because it 'looks' like it should go in the other way around!
For the GH:WT guitar (havent tested others) you need to hold the guitar so you can read the Guitar Hero logo normally. Place the battery in so that you can see the corner with the "Insert This End >" text facing out, on the top-right side. "Guitar Hero rechargeable battery pack" should appear upside-down.