MacBook - Not Powering On
Your computer will not boot.
If your computer beeps three times, there is a RAM issue. Either you have insufficient RAM to boot, or the RAM you do have is faulty. First, access the RAM slots (provided your machine has user replaceable RAM) and ensure you have RAM installed. If you have two chips, first reseat them and try again. If that doesn't work, try one chip at a time to see if one of the chips prevents the machine from booting. If none of these work, you may have a bad logic board.
Bad power adapter
If your battery is not charged, is completely dead or is removed from your machine, please make sure you are using your original Magsafe adapter! There are three different adapters 40W, 60W, and 85W. If your machine originally shipped with an 85W adapter, he 60W adapter will keep a charged battery from draining but does not have enough juice to provide full charging functionality. If your power adapter is bad, the computer will run off a battery, but it won't charge. If your battery's charge is too low, it will be difficult to diagnose a bad power adapter. The easiest way to test this is to borrow either a battery or power adapter to test in your machine. If you have the same problem with another power adapter, your problem is most likely the left I/O board. If you have the same problem with a fully charged battery, you most likely need a new logic board.
Thermal Sensor Issues
If the fans run at high RPMs, but the computer does not boot, there is probably an issue with the thermal sensors. First, ensure that the thermal sensors are plugged in. If they are, try replacing the thermal sensors. If this does not fix the problem, the logic board most likely needs to be replaced.