Any battery should work, as long as it meets the specs (same voltage, number of wires, ...) and dimensions to fit unless you fancy reading with an open case. If it's not the exact same connector you can recycle the one of your old battery by connecting the wires.
Another reader, but similar battery issue:
https://www.mobileread.com/forums/sho...d.php?t=187460
Maybe someone has already done the replacement for the Aura HD specifically and can link to a more suitable replacement product.
Other possibilities for erratic behaviour: bad internal sd card (or just a damaged filesystem; could happen if the reader got stuck during an update), bad usb cable, loose connector somewhere, water damage... I hope that's not it though.