Frustrated, single, virgin and male. Feeling really lost. What do I do?

Just like the question states. I have no idea what to do anymore. I'm 19, going on four years single, haven't had sex. It may sound vulgar, but I can't tell what I'm getting more tired of: Being single, or being a virgin. I really want a girlfriend, but I don't want one just so that I can have sex. I'm more into the companionship aspect of a girl-guy relationship. If I were asked to engage in that, I cannot tell you how careful I would be, and I'd probably be very hesitant at first. But lately, I've been getting really frustrated in the sexual sense. I'm not a hump-and-dump type of guy, and I don't know a thing about going to bars to pick up a one-night stand or going to a prostitute, and I care for doing those kinds of things even less. But I'm starting to feel like I'm backed into a corner here. I feel like I need to get laid worse than a panel of sheet rock. If you've ever seen Kevin Smith's movie Dogma, you'd hear that Jay masturbates more than anyone else on the planet, but sometimes I think I beat him, so to speak. I really wish I could make myself stop wanting this, but I can't. What do I do? And please don't suggest going to a bar or picking up a prostitute. For one thing, I can't stand the idea of just going to a bar or a dance to "pick up chicks" because I like to feel a connection. And there are so many reasons why getting a prostitute is a bad idea, it's not even funny. Also, I should mention, I know sex isn't everything, but good luck trying to convince the body of any male pre-twenties person of that. While the brain may not want it all that much, the body wants it like a madman.