How can I insulate my basement so rain doesn't leak in?

Chances are you need to regrade the soil to slope away from the structure. In addition, I would also have a consult with a foundation specialist to see if you have any water intrusion issues that might compromise the structure. Here is how to hire.

https://www.consumer.ftc.gov/articles/0242-hiring-contractor

Gutters would help too.

I used a product called dry lock and painted the whole interior of my cement walls.

If the walls are the problem, Drylock paint is good, and fill any cracks first with hydrolic caulk. If the water is coming up through the concrete slab, seal it with a concrete sealer.

Keeping your gutters clean and free of debri is very important, and I added long extensions to the downspouts to move the water further from the house since I live in the rainy PNW..

I'll echo all of above... We solved a lot of our wet basement issues by making sure downspouts and gutters drained away from the house and doing some grading ourselves with a shovel, a rake and some hard work.

The interior fixes have been ok, but the best results have come from working outside to keep water away from the house in the first place.

Good luck

First, check to see if the downpipes (the pipes that come from the eveatroughs down to the ground) outside of the house lead at least 10 feet away from the foundation walls. If they drain at the foundation, you can buy some at your hardware store in 10 foot lengths and install them yourself. This could aleviate your basement leak problems.