I think you should get therapy, first and foremost. Your depression sounds like a serious problem. It's going to be hard to find ambition like that, and sometimes it takes more than trying really hard or thinking positively to get anywhere with something like this. You need help. You're not in a good place and there's a negative feedback loop that's fueling your desperation and hopelessness.
And if you can manage it at all, don't leave your job. I know a lot of people are down on you in this thread (not that they're not giving perfectly legitimate criticism), but I think you're not doing as badly as you think you are if you're managing employment at all. You didn't really say anything about why you want to leave, but you have to really identify how much it's about the job and how much it's about you. Sometimes it can be really hard to tell the difference and you can think the job sucks when in reality almost any job would end up sucking the same way. You don't want to put all of this effort into a new job only to end up feeling the same way about it or even worse. And you don't want to risk losing the stability you have now for an indefinite period of time. That is, unless your mental health absolutely requires it, in which case you'll be advised to apply for disability insurance.
Now this is leering off topic, but I also think you shouldn't get bogged down by all this alpha or beta male crap. People are using it figuratively to begin with, about it being more of an attitude and confidence thing than actual roles in society (could you imagine how stupid it'd be if we actually had alpha males anything like seen in other animal groups?). But I say drop it altogether. You don't have to stand above everyone else to be useful. People take on very specialized roles and there's room for pretty much everyone to be useful, unique and recognized, both in the workplace and in relationships.
That's just my subjective advice filtered by my own experiences though, take it as you will.