Well, I have an 8GB SDHC card in my Kindle 1 and I'm not having battery problems. Now that I have a Kindle 2, it's my primary reader and the K1 is my back-up.
I turn it on every few days to download new books I've purchased. I leave Whispernet off until I need to download. It's been off the charger for a few days and is still about 85-90% full.
I'm surprised the new battery didn't work. I don't have an answer for you but I'm curious as to how long you've had your K1? Did the battery gradually get worse or did it happen very quickly?