Due to the few number of parts, troubleshooting the iPad is fairly straightforward.
No matter what you do, you can't get your iPad to turn on.
If your iPad's problem isn't so easily solved, read on.
If your iPad won't turn on, especially if it has not been used recently, you may simply have a drained battery. Plug your iPad into your computer or AC adapter and see if anything happens. Ideally your iPad will recognize it has been connected to a power source and charge its battery. If it will no longer charge, the battery must be swapped with a replacement battery.
It is possible that it appears nothing is happening because the display is bad. If the battery is working properly but nothing is visible, it is possible the display is bad and must be replaced.
Ultimately, if the display and battery are not the culprit, check all the connections from the display to the logic board. If they are connected properly and there is still no life, the logic board most likely needs to be replaced.
Your iPad is not recognizing the touch input on the front panel
It is possible that the touch screen is bad. If so, you must replace the front panel (which includes the touch screen and digitizer).
If replacing the front panel does not restore touch input, the logic board must be replaced.
Your iPad turns on and appears to work, but when you plug in headphones or speakers, the audio doesn't play properly.
It's unlikely your headphones or speakers are bad, but it's worthwhile to eliminate these as the source of your problem at the beginning. Try your iPad with another set of headphones or speakers just to make sure that the problem is with your iPad.
The most likely cause of audio output problems on the iPad is a bad audio-out jack. First try a full restore on the iPad to make sure it is not a software issure. If that fails to work, try replacing the audio jack. If that doesn't solve the problem, your logic board most likely needs replacement.
Your iPad displays the text "Use iTunes to restore" on startup
It isn't often that Apple gives specific directions about how to fix your problem! Restoring the iPad will erase everything on it, so make sure everything on the iPad is stored elsewhere prior to restoring. To restore, connect your iPad to a computer with the latest version of iTunes installed. When your iPad appears under the devices menu, click the restore option under the summary tab. If you haven't backed up your data already, choose the back up option from the pop up window. Click the restore button to restore your Touch to factory spec.
If attempting to restore the iPad and diagnosing does not fix the problem, the issue is probably the logic board.