Dell Venue 11 Pro 7130 Won't Power On/Has Blank Screen

Sigh. I'm a bit desperate. Please bear with me.

My Venue is about 1 year old, and while it has been a bit glitchy (occasionally powers off unexpectedly, won't wake from sleep mode, and most annoyingly, has a loose power port that makes charging rather CHALLENGING), it works well enough to be enjoyable. However, today, out of the blue, the tablet won't completely power on. I press the power button, the tablet vibrates, the charge light is on, the tablet heats up, the fan whirrs, but all I get is a blank screen. I've tried holding down the power button for 20 seconds and holding both the power and up power buttons, but neither work. 

Has anyone else had this problem? How can I fix it? Conveniently enough, my warranty expired less than a month ago. Yippee.

I'd appreciate any help you could give me.

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