You just need a serial number. You can easily find some on ebay or in youtube unboxings. There are many guides here on how to find one.
Message them, that your microphone wont work properly. They will give you a few steps to fix the problem, but in your case the steps wont help!
 
They will forward you the information of a partner repair center that they have in most countries. I did this now for the second time, so keep in mind I am not omniscient in this case.
Just be polite but annoy them that you are not willing to pay the fees for the shippment to the repair center. Whatever they will write you, tell them that you are a famous youtuber, or podcaster and you buy Rode mics since forever because of the good quality and the reliable support. And for that expensive price, you expect that there are no follow-up costs for you.
 
I thought at first they send me a shipping box so I can box them, but they arent allowed to do that (stupid company policies) so they will send out a replacement after you give them your adress (do it only when they ask for it).
 
For me it was like 10 emails to get the shit done (you will have contact with the support in Australia, no matter from where you are), I think if you call them you could do it better than me, but they reply pretty fast (good job Rode support if you will read this one day). I got like 3 answers per day. Be agressive but polite. Do not accept a no and play the customer-is-king card.
 
In my second try I got two mics at once (Rode USB and Rode Podcast ((recommend the first one, its awesome)). Please dont fuck them to hard, so others could also get the opportunity to se them. And keep in mind, they are a great company, so please have a bad conscience. They dont deserve us, or at least some of us that fucks them 10 times in two weeks.