It's a RAM problem, 13" models have 2GB soldered memory and the RAM is not upgradeable or replaceable. 15" and 17" have a 4GB maximum with two slots and you can replace the RAM on those.
"I have found solution, the problem is so small and funny, unbelievable small.
I had problem few days, totally black screen and only three beeps in intervals, no boot.
And i don't wanna to give a lot of money for nothing so i decided to do everything which i know and to fix it or trow it in a garbage.
I have tried thermal paste, have checked the memory chips on logic board, soldered the new one, but again the same.
The problem was that thermal sensor which is on the small board and glued to the logicboard (i don't know why they do like that) have take apart from it and touching the metal part of cooler and making a short circuit. I had glued back again, put the paste and cooler and, woala, air is on the air again hehe
"This thread has become a dump for MacAir 3 beep solutions so here's my addition: I worked through the following non-invasive techniques (most listed above) a couple times each and after doing 5) it started booting. Maybe they worked as a combination or maybe it was 5 that did the trick. If none of these had worked I'd have tried the Thermal Paste solution above. However, if non-invasive works, who am I to complain! Hopefully this compilation helps someone!
UPDATE: This happened to me a second time two months later: I have found a firm fix for my issue now:
1) power off, plug in power cord
2) Hold (left side) command + (left) option + P + R
3) while holding them, tap power and CONTINUE HOLDING the four buttons in 2
4) Computer will make a startup sound, KEEP HOLDING, computer will turn off, KEEP HOLDING, computer will startup again, you can let go only AFTER the second startup or even third startup.