Wow, I'm late.
Try plugging the calculator into your laptop. This should make it turn on if the [on] key doesn't work.
You could also try turning it on, then press [2nd] then hold down the up arrow until you see a cursor flashing. If it's been 10 seconds and you don't see anything that's not good.
Try removing the backup battery (and replacing it) and one of the AAA batteries. Then wait 10 minutes, then replace the backup battery and AAA battery. This should force the calculator to turn on.
If nothing worked, then it sounds like you have a defective calculator. :\