MacBook Pro Is Beeping Constantly And Won't Turn On

The big question is: What does "constant" mean?

Beeps at startup usually indicate a hardware error; the pattern of beeps tells you what type of error is causing the problem. Apple has a tech note describing the patterns and how to repair the problems:

Mac computers: About startup tones

The two broad categories are RAM (memory) problems and EFI ROM (firmware) problems. If it's RAM, you've got a big problem; the memory in a MacBook Air is soldered to the logic board, and the logic board will have to be replaced. If it's EFI ROM, the tech note describes how to do a ROM recovery.

MacBook Air Models A1237 and A1304 Logic Board Replacement