Don't sweat if it takes a while, and don't compare yourself. Not everyone is good at interviewing at first. Just try not to burn out - when I first started, I would go crazy studying for a month, then burn for a month. Rinse and repeat. In the past months it's been a slow, steady, and consistent effort to improve. I don't have a CS degree (ECE) and went to a state school (but it has a good rep) and my previous job was at a tiny no-name company. Oh, and you get used to the bullshit. My advice: network. I got a lot of interviews (and my current job, and another offer) due to networking. I went to a lot of meetups at my scene (NJ/NYC).

Your experience will count, it's just you've narrowed the pool of opportunity. Web Dev is just a bigger target with more hiring going on.

If you apply to a Web company without much web dev experience (or knowledge) then yes, it'll count for less.

But that's true of anything. The bay area is probably the easiest place to get hired in tech right now as an engineer.