91 degrees is not uncommon for a laptop chassis when under load.[br]
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Troubleshooting Steps :
# When you start it, try shining a flashlight closely on the display. If the backlight is out, but the machine is somehow on, then you can see a faint image. Although this seems unlikely if there are no lights on the keyboard or indicators.
# If you can, try removing the battery and plugging it back in.
# Attempt plugging it in without the battery attached. Look for any indicators.
# Do a CMOS reset. (Removing the coin cell battery or if it does not have a removable one)
# Start disconnecting peripherals and then internal cards. !!!ONLY IF YOU ARE COMFORTABLE!!! The only reason I suggest this, is a unit will typically be able to at the very least produce a POST code or go to BIOS even if the RAM, SSD, and network cards are disconnected from the system. If it cannot do this, then the issue likely lies on the mainboard.
These steps are the basics for troubleshooting a laptop like this.