Your battery may be malfunctioning. Try plugging it into the charger (and letting it sit for a few hours) before turning it on; if it turns on while plugged in but turns off when unplugged, it will need replacement.
To replace the battery, you will have to remove the entire back panel of the tablet and carefully remove the cables crossing over the battery, then replace the battery and move the cables back to their initial position.
If it still doesn't turn on while plugged in, your motherboard may have a faulty component such as a malfunctioning RAM stick. Generally, it's easier to replace the entire component than to replace individual parts, so you will have to procure a new motherboard and install it.
A full guide for both will be available here:
HTC Flyer Troubleshooting
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