I would definitely return it. I got mine directly from BioLite last summer, and I've used it half a dozen times since then.
If you look at the battery pack while it's mounted on the firepit itself, the LEDs below the power button should be the Battery Charge indicators. The ones above the power button are the Fan Speed indicators. When you hit the power button once, it should display the current charge level. Pressing it a few more times will cycle through the fan speeds from low to high and back around again. If you plug in the micro USB input for charging, the Battery Charge indicators should blink continuously while charging.
If you're not getting any LEDs to light up at all - whether plugging it in to charge, or when pressing the power button - then I'd definitely return it. Sounds like you've got a defective unit to me.
Good luck with it!