You may be passionate about it, but if you don't have the skills to contribute, setting the goal of contributing to that product without any intermediary wins is guaranteed to demotivate. Put another way, lets say your business is an automotive repair shop, but you're not a mechanic. You are passionate about fixing cars and work with a bunch of people who are really talented at fixing cars so you want to jump right in. If your first task is to repair the inner workings of a combustion engine, you're going to give up before you even start. Start by learning how to work a wrench and change tires. Assuming you are truly passionate about fixing cars, completing this simple task will provide you with an emotional reward. Move to something slightly more complicated that will require you to learn something else.
It's not a perfect analogy -- you could ask a 100 developers what wrench to pick up and get 100 different answers ranging in complexity, power and learning curve -- but the idea is to avoid tasks that have a huge up-front learning curve that would result in demoralization and disinterest.
I think you need to consider whehter the issue is that you see the value in programming and can see yourself enjoying that role and adding value in that way, or you are just having trouble seeing the value you are providing in your current role as, apparently, a non-technical co-founder.
> I can go get more users and sign them up all day
So-called "soft" skills like getting users, signing them up, and learning what they want that would make the product more valuable/attractive to them are important, value-producing skills that many technical people don't have. You shouldn't feel like an "idiot", or like you don't have value, because your skills are there rather than in writing code.
Also ask yourself, does my co-founder even want me touching the code and servers?
That or really stick to your guns and get into coding for real. It seems that the major problem is that you lack the proper motivation to learn. So why not ask your co-founder if there is some small aspect of the website that you could work on in your free time?
Get your co-founder to set you up on your own branch so you can work in isolation and learn how to do that small feature step by step. This way you'll have the motivation that your feature might someday make it into the final product. Just make sure to have your partner review your code and live with the fact it might not be good enough to use (yet).
Practicing on features used in real projects can really help you learn at lot.