I have read over the beginners guide multiple times hoping for something that might help me.
When I power on my device, I get the FFF triangle for a few seconds. Then it begins to loop that screen for a few seconds then reboot. I am unable to press the power button (either once, multiple times or holding the button down) to enter into recovery.
Windows is not discovering my device when I connect the USB. In between loops it will occasionally pop up the Found New Device wizard. As for not being able to discover my device - I was told this was related to the ROM. I could only mount the storage from within TWRP which I am unable to access.
Is there anything else I could tell you that might help you understand what is happening? I'm not a android pro by any means but I'm not totally technologically inept either.
Thanks again for any advice.
Based on what you are describing, I think your battery is (near) dead. The reboot is probably happening because the CPU not getting enough power. I would suggest plugging it into your stock AC charger and leaving it alone for a while to see if it will charge back up.
The bad thing is that the Kindle Fire needs to boot up to charge because the ramdisk handles the charging operation. If your battery doesn't have enough juice to get the CPU going, you might find yourself in a catch-22.
The AC charger is your first, best bet to get your device fixed up.
EDIT: Most users I've seen report this problem have been able to get it to charge with the stock AC charger. However, if that doesn't work for you, take a look at this thread...
http://xdaforums.com/showthread.php?t=1392693&page=23
start at #226 and read about 20 posts or so into it.... Good luck!