Hi NullNix, thanks for your response!
When I saw the error the thought did occur to me that it might be a problem with the flash memory itself rather than anything else, but thank you for basically confirming it for me!
I honestly think, given what you've said, that the battery draining was likely never the root cause of the problem and that the battery was dead purely because of the age of the device (it was the original battery) and the time it was left idle. There's nothing visually that I can see on the motherboard or case in terms of battery goop, corrosion or damage, so this is more than likely an internal hardware failure.
It's a shame that it's not recoverable, but I guess that's just how things go sometimes. I can't say that the device didn't have a good life though; I originally gifted it to my Mum for Christmas way back in 2010 and it was used daily for ~7-8 years before she eventually upgraded to a Paper White Kindle model and this one boomeranged it's way back to me last year!
It's unfortunate that it's not something that can be fixed, and I'm a little sad that I wasn't be able to, but there's a limit to everyone's abilities and I can at least say I tried everything I could to rescue it!
I'll likely look into buying a new kindle in the next few weeks, as I'm quite keen to get back into reading. And, on the plus side, now I have an FTDI Serial Adaptor in my arsenal to use on some potential future projects!
Thanks again!