iPad 3 stuck on the iTunes logo
Try holding both the power and home buttons at the same time for about 10 to 30 seconds.

EDIT 1: Try to connect it to iTunes on your computer. iTunes may offer to try to fix it for you.

EDIT 2: If all else fails, check out the "If your device gets stuck during startup" section of this Apple support page.

EDIT 3: If nothing works at all, try using the Apple's Recovery Mode. If this fails, you should contact Apple Support directly as it might be a hardware issue: http://www.apple.com/support/