Take the battery out.  Plug the AC adapter back in.  If it doesn't chime/screen pop up on schedule, press the hard reset button on the back.  If that doesn't work press it once again.  For God's sake don't just go out and replace the logic board lol.

Normally I get that sound [it's not precisely the same but it's very similar] when I experiment with my battery rebuilds.  If what I said above doesn't work immediately, leave it with all power to it disconnected including the battery for an hour or two (probably less in reality) and then try again - again without the battery.  There's almost certainly no harm to plugging the battery in once it's started, though.

If none of that works the first step would be the replace the power board; however, while it is possible it is a logic board problem, that type of repetition suggests repeated attempts and failures to turn on (I think - probably to draw sufficient current).