This issue could be either software or hardware related. When the LeapPad does not proceed past the LeapFrog logo screen due to a software issue, this can be corrected by the LeapFrog Connect application with the below steps.
1) Begin with the LeapPad powered off and the LeapFrog Connect application running on your computer. If you do not have the LeapFrog Connect application installed on your computer, you may download it at www.leapfrog.com/connect
2) Starting with the LeapPad off, simultaneously hold down the right directional pad, home button, and the down volume button.
3) Turn the power on while holding these buttons. This will bring up the tune up screen.
4) Once you see this screen connect the USB cord to your computer.
If the reason the LeapPad was stalling at the logo screen was software related, the LeapPad should boot up normally once the sync is complete.
If the LeapPad's sync with LeapFrog Connect will not complete (sync progress will stall at 40% or earlier) this would indicate a component failure is the root cause of the issue, in which case the LeapPad would need to be replaced. If your LeapPad is still within the one year warranty period, please contact customer support for warranty assistance.