Another update. I got super lucky on ebay and found a listing for a working and good condition DSi XL that I thought, "can't hurt to try and bid". Got it for cheap because it closed in the middle of the night. Arrived a few days ago and unlike the previous one, ACTUALLY holds a battery charge.
So now I'm going to actually sell my old faulty one. What is a decent price to ask for it? It has had the bottom touch screen replaced, the condition on the plate around the buttons are worn and it only really works when you plug it into a power charger which means the portability is crippled. I know I'll never get top bucks for this but I thought it can't hurt to check what's the best asking price.
Just set it as a Bid auction and describe it in detail so people know its condition. Don't be half truthful, like the seller you bought it from. From what you described, I wouldn't buy it for more than 15 bucks, but that's just me.
Edit: Wonderful listing; so thorough.