My laptop will not switch on. The battery will

if the battery charges, it does indicate that the battery and AC adapters are okay, try removing the center hinger cover/panel, then attempt to power on the system. You can also try to remove the battery and test it with just the AC adapter. if this fails, it would indicate a motherboard failure, but you can try to isolate it by reseating or replacing RAM first, or try removing all devices that can be disconnected like the hard disk and dvd/cd drive.