OK, I have an older MacBook air model a1237 that chimes then about 10 seconds later 3 beeps over and over. I pulled the logic board and looked it over with a magnifier several times and it's real clean no parts look bad so I put on new thermal paste and still have 3 beeps BUT I figured out by timing the boot process, turn it on and after it chimes and when the screen lights up push power to turn it back off then hit power a second time and it boots fine. I did this about 20 times and it boots that second time every time. So when I want to use it, hit power, wait for the chime and hit power to turn it off then hit power to boot. Don't know why it works but for this MacBook, it just does. Tried booting with the disk drive out and same thing so it's not a software issue, something with the board but at least I got it to boot. Just FYI, when you power it on and it chimes and as soon as the screen lights up it is approx. 8 seconds and you should see the apple logo.