So, as you might imagine, all of my motivation/inspiration to get up and write code and study math has to come directly from me. And all of the distractions--invitations to go to the movies, or go out and eat, or hang out at someone's house and ultimately do nothing--come from the outside. It's so easy to give up on a project for the day when everyone's getting together to hang out, and you're the only guy who keeps saying "Nah, I need to stay home and get some work done." It's frustrating and, at this point, extremely lonely. I really only have one person I can talk to about my interests, but he and I have only just met each other, really.
This seems to me like you are complaining about something you chose for yourself.
To word it a somewhat provocatively: It's not that you have to be the stereotypical lone fat geek who lives in his mother's basement, whose only contacts are the other geeks in the comic book shop, whose only social interaction is playing D&D, and who has never dated a girl to qualify as "computer dude".
It is perfectly possible to work in IT and do something that does not require a computer at the same time -- go out, do sports, have a wife and family. These are not antipodal or mutually exclusive. They only become that if you choose something different.
You don't have to stay home and "get some work done" when it's cinema evening for everyone else. The computer won't run away while you're not at home.
You don't have to lower the blinds so the sun isn't interfering with watching youtube -- you can just as well go out in the garden and do BBQ with your neighbours. Or, plant a tree, trim the roses, mow the lawn.
You don't have to talk geek stuff with people if none of them is interested in it. There's a plentitude of other things you can talk about or do.
Oh, and you don't need to bring your smartphone when you're out hiking/fishing/drinking beer with your friends. No puppies will die if you forget to twitter about it and if you don't upload the photos to facebook.
If you notice that you feel lonely, you've already done the first, most important step (insight/admission). Now you only need to decide that you want to change your situation, and then you have to act according to that decision. OK, that sounds like something from Oprah Winfrey, but it's really as easy as this.
Chatting with some strangers on the internet (even over Skype) won't get you anywhere. Doing real stuff with real people will.