Toshiba P55W-B5112 would power off when battery still had a charge and would not power back on though when plugged in the charging light would light up. Replaced the battery thinking that was the issue, but the same thing would happen. The only way I could get it to power back up was to disconnect the battery which is inside under the back cover. (Note: if you decide to do this yourself on this model, you need to be very careful as the power button cable is connected to the power button board attached to the back cover and needs to be disconnected before you can fully remove the back cover. Open the back cover only at a 45 degree angle or less until you get this cable disconnected from the motherboard.) Found that if the battery was left unplugged and only used the power adapter that this wasn't an issue. Concluded that the most likely issue is that the battery port on the motherboard is shorting out. Will be replacing the motherboard and if that fixes the issue, as I'm fairly certain it will, I will edit this to let you know. Hope this helps someone out there.
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Edit: Motherboard replacement worked beautifully, so bad battery port on the motherboard was the culprit.
Toshiba P55W-B5112 would power off when battery still had a charge and would not power back on though when plugged in the charging light would light up. Replaced the battery thinking that was the issue, but the same thing would happen. The only way I could get it to power back up was to disconnect the battery which is inside under the back cover. (Note: if you decide to do this yourself on this model, you need to be very careful as the power button cable is connected to the power button board attached to the back cover and needs to be disconnected before you can fully remove the back cover. Open the back cover only at a 45 degree angle or less until you get this cable disconnected from the motherboard.) Found that if the battery was left unplugged and only used the power adapter that this wasn't an issue. Concluded that the most likely issue is that the battery port on the motherboard is shorting out. Will be replacing the motherboard and if that fixes the issue, as I'm fairly certain it will, I will edit this to let you know. Hope this helps someone out there.