My notebook won't turn on. When the battery's in, the green light comes on momentarily then goes off and the amber light comes on then goes off. When the battery's not in the only the green light comes on momentarily. The charger has been tested and is fine.

I've had this problem before. It is likely that you have a bad power supply on your laptop. It is often a costly repair, but should be covered under warranty. If the charger seems to be fine (meaning that it was tested on another laptop and not just checked with a digital meter), then you may consider upgrading!
Hope this helps! Rate my solution!

First, remove any external device as well as the ac adapter and the battery. while the ac adapter and battery is out, press and hold the power button for about 15seconds. then reconnect any power source and turn on the system. if it still doesnt turn on, remove memory, expansion cards, hard drive and optical drive then turn on the system. if it's still not turning on, the motherboard is faulty. but if it do turned on, reconnect the removed components one by one so you will determine which component is causing the issue. hope it'll help. good day. =)