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Step 1
Unplug the AC adapter.
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Step 2
Turn on your laptop. If it does not boot, plug in the adapter. Try again. If the laptop boots up, you now know that the laptop works. Continue to step 3. One possibility is the AC adapter may not be working correctly. This would not only stop the laptop from booting up, but it would not be charging the battery. Take the laptop into a shop. See if they will lend you an adapter to see if it is the problem. If the laptop still does not boot, there is a good chance there is a major problem with the laptop.
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Step 3
Feel if the battery is hot. It should be warm but not hot. If the battery is not even warm, there is a very good chance that it is not being charged properly. Again, this can be the adapter or a bad battery. If the battery is very hot, there is most likely a problem with the battery. It is probably best to replace the battery.
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Step 4
Check to verify the battery charging LED is blinking. If the LED is not blinking, the battery is probably dead.
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Step 5
Verify the battery is secured correctly. Check the latch for the battery on the bottom of the laptop. It is easily identified. It may even be a good idea to remove the battery and reinsert it into the laptop.