Post update, Dell-Cares dispatched a replacement battery. 
Hello. I got a Latitude 3400 that my school was selling off, but after a few months of usage, I’ve noticed the battery is under 50% health, and it really shows; I might be able to last four hours on minimum brightness and one tab open. I can get a second charging cable for when I’m out an about, but what I’d really prefer is a battery replacement. However, these replacements only seem available on the US store, which of course doesn’t allow shipping to Australia. Is there any other way I could get a battery replacement, or do I have do go down the path of carrying a power brick with me everywhere?
Latitude 3400 Battery Replacement in Australia