Battery charged, laptop sometimes won't power on when unplugged

Step 1:
Take the battery out, plug in the charger and see if the laptop works. If it works, the battery may be the problem. Check the AC Adapter
Check to make sure the adapter is plugged securely into the wall outlet, connected firmly to the adapter box and to the back of your laptop. Most AC adapters have a little light in them on that rectangular box in the middle of the cord that lights up when it's getting electricity. If that light isn't on, try a different outlet. Check your fuse or circuit breaker box and plug a different device into that outlet to make sure there is power to it. If it still does not light up, your adapter could need replacing. Also check the adapter box for signs of warmth, as it will generate heat when it's plugged in. No heat means no power.

Remove the Battery Sometimes it's as simple as a seated battery. Remove the battery entirely and clean out any dust, lint or hair that may be clogging the connectors and preventing a proper connection. Reseat the battery securely and make sure the little locking pins that hold your battery in place are securely fastened and there is no movement. Unplug your laptop while it is running. If it still works, the battery has been charging. If it shuts off, or doesn't hold a charge very long, you have a bad battery. Unplug your laptop while it is off, then try to turn it on. If the battery is bad, your laptop probably won't turn on at all. Turn off your laptop's screen-saver when testing its battery. The screen-saver will conserve the battery and not give a clear time frame for how long your battery can really last. Click the battery icon on your laptop when it is unplugged. It can tell you how much battery life you have available. This icon is usually located in the bottom right corner of your screen and will provide the percentage of battery power you have left. Keep track of the time it takes to go from 100% charged to 1% charged. If this takes less than an hour, your battery is probably beginning to fail. You can also try this every week or two to see if your battery holds a charge for shorter periods. Factor in the amount of time you have used your laptop. Most laptop batteries last 2 to 3 years or about 500 charges. Wait a few days before determining whether a new laptop battery is faulty. New batteries sometimes take a few charges to build up to their maximum run time.

POWER SUPPLY & BATTERY PROBLEM
If the laptop battery is more than 3 - 4 years old then the battery could be worn out. Rechargeable batteries have a finite number of charge and discharge cycles and will lose their charge capacity over time, i.e. won't charge to 100% and gradually the charge reduces until the battery won't charge up at all. OR The battery shows a 100% charge but when the adapter is disconnected the battery drops off to zero capacity in a very short time. If the battery drops to an unacceptable charge level then the battery needs to be replaced. Rechargeable batteries will fail if stored in a discharged state for long periods.

If thelaptop battery is more than 3 - 4 years old then the battery could be worn out.Rechargeable batteries have a finite number of charge and discharge cycles andwill lose their charge capacity over time, i.e. won't charge to 100% andgradually the charge reduces until the battery won't charge up at all. OR Thebattery shows a 100% charge but when the adapter is disconnected the batterydrops off to zero capacity in a very short time. If the battery drops to anunacceptable charge level then the battery needs to be replaced.

POWER SUPPLY & BATTERY PROBLEM
If thelaptop battery is more than 3 - 4 years old then the battery could be worn out.Rechargeable batteries have a finite number of charge and discharge cycles andwill lose their charge capacity over time, i.e. won't charge to 100% andgradually the charge reduces until the battery won't charge up at all. OR Thebattery shows a 100% charge but when the adapter is disconnected the batterydrops off to zero capacity in a very short time. If the battery drops to an unacceptablecharge level then the battery needs to be replaced.

If thelaptop battery is more than 3 - 4 years old then the battery could be worn out.Rechargeable batteries have a finite number of charge and discharge cycles andwill lose their charge capacity over time, i.e. won't charge to 100% andgradually the charge reduces until the battery won't charge up at all. OR Thebattery shows a 100% charge but when the adapter is disconnected the batterydrops off to zero capacity in a very short time. If the battery drops to anunacceptable charge level then the battery needs to be replaced.

It sounds as though you have a defective battery. You will have to go through Macintosh for assistance.

Battery could be dead and won't hold another charge. Batteries only last for so long until you have to replace them. If you laptop is ok with the AC Adapter & Power Cord meaning it boots and allows you to work in windows, then the battery is definitely dead.

Not really, the older NiCad batteries get a memory effect if you keep charging from a half charged state, but modern Lithium batteries do not suffer from this problem.
If thelaptop battery is more than 3 - 4 years old then the battery could be worn out.These rechargeable batteries have a finite number of charge and discharge cycles andwill lose their charge capacity over time, i.e. won't charge to 100% andgradually the charge reduces until the battery won't charge up at all. OR Thebattery shows a 100% charge but when the adapter is disconnected the batterydrops off to zero capacity in a very short time. If the battery drops to anunacceptable charge level then the battery needs to be replaced.

Laptops are so integrated that usually a system failure that involves power issues such as in your case where you cant get it turn on with anything on the screen mean the mainboard (motherboard) is damaged. This usually leads to buying a new laptop or paying for the board to be replaced which usually costs as much as the laptop.

Ifthe laptop battery is more than 3 - 4 years old then the battery could be wornout. Rechargeable batteries have a finite number of charge and discharge cyclesand will lose their charge capacity over time, i.e. won't charge to 100% andgradually the charge reduces until the battery won't charge up atall. ORThe battery shows a 100% charge but when the adapter is disconnected thebattery drops off to zero capacity in a very short time. Ifthe battery drops to an unacceptable charge level then the battery needs to bereplaced.