I'b make sure the rain water was pure. I live in an earth contact and believe it or not, something likes to crap on my roof. Probably a coon or possum. I collect rainwater but only for watering with.
Try the tap water and see if it works. Mine does. If not, get some distilled water.
Here's how I make my starter for anyone who is interested.
ACTIVE SOURDOUGH STARTER RECIPE:
2 tbsp. rye flour (or flour of your choice)
2 tbsp. water
*NOTE: I recommend whole grain flours. AP and bread flour have been highly processed and are not as nutritious as whole grains. I prefer stone ground flours like Bob’s Red Mill, Hodgson’s Mill, etc.
Add flour and water together in a pyrex measuring cup or small jar and cover with plastic wrap. Stir daily 2 or 3 times a day and you should begin to see activity (bubbles usually within 24 hours) and detect a slightly sour smell. Once you begin to see bubble forming in the starter, you need to start feeding it daily.
To feed the starter, add 2 more tbsp. of water and 2 tbsp. of flour on the first feeding. By the second day, you'll now have about 1/4 cup of starter. When you feed it each time, you are doubling the amount you're feeding it so now you'll need to add 1/4 cup of water and 1/4 cup of flour. As you can see, you can end up with a lot of starter very quickly so what you do is when you get the amount the recipe calls for, you throw out half of the starter each time you feed it. If you have 1/4 cup of starter, throw half of it away (1/8 cup) and add 1/8 cup of water and 1/8 cup of flour. You can give the discard starter to friends or refrigerate it for later use. You only need to feed it monthly in the fridge. Always make more starter than the recipe calls for so you can save some back for future batches. It will keep a long time in the refrigerator and the older it gets, the better it gets.
At some point you might pull it from the fridge and notice a grayish liquid on top and it will smell like alcohol. It is alcohol and it’s because your starter is very hungry. This is part of the flavoring and initial hydration so stir it back in and start feeding the starter again for several days to get it nice and active for your next baking day. The alcohol cooks off during baking.
Questions? Ask me.