If the Razer Blade turns off when the power adapter is unplugged, it is a sign that the battery is dead or the lithium inside the battery pack has been depleted.
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With the adapter plugged in, verify if the Blade is holding any charge in the battery.
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Navigate to Start > Settings > System > Battery.
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See if the battery overview is showing any charge left.
If the battery shows a charge:
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Ensure the charge of the battery is above 50%. If the charge is below 50%, charge the laptop above 50% before proceeding.
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Once the device is sufficiently charged, unplug the power adapter from the device.
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If the device turns off after unplugging the adapter, the lithium inside the battery pack has been depleted.
If the battery does not show a charge, the battery is dead.