What they said!
Heck, I myself am a geeky anime-fan, rennie, and big rpger girl. We are out there. I promise
And I will reply to your ramble with one of my own.... (sorry ~ I'm prone to long posts when tired.)
I've told friends (and I've seen it work - on others and myself) just work on being happy with you. Is there something you want to improve about yourself? (for you, not because of what others think)? Start working on it, a little at a time (most things don't change quickly). Something you always wanted to learn? Take a class. A cause you support? Volunteer. Heck, if nothing else take some art supplies to the park or hiking and find a nice spot to sit down and draw/paint! But get out there.
Don't go out looking for love. No one else will complete you (despite what the love songs say). Because if you're not happy before the gf, you still won't be happy after. When you go chasing after love, people pick up on it and it tends to come off as "desperate". When you are happy with with yourself, and focusing on doing things you enjoy, you are confidant and, well, happy. People like being around confidant, happy people. And then one morning, you'll wake up, stretch, sit up in bed,and **BAM** the 2x4 of love will hit you right between the eyeballs and you'll stagger around the rest of the day wondering what just happened. And it will probably be someone you hadn't been looking at in that light.
Don't worry about game. It gets old. It sounds like you want a relationship, not just a fling. From what I've seen, game is used to get the latter. Just help yourself get over your shyness. Being one who can be painfully shy myself, I know it's not easy. But just try saying "hi" to the girl standing in line next to you. No witty banter. No come-ons. No pressure. Just "hi", or "hey". And you can leave it at that, or compliment her shirt/purse/necklace/pick an accessory. Even if it's indirect - "I love that shade of purple" <- but only if you really do. Or comment on the wonderful sunshine today. Simple little things. And don't be upset if nothing happens. Most of the time, you'll just say hi to a stranger. But you might start a conversation. Many girls suffer similar issues as you do, and won't bite your head off for saying hi, and those that do, well, do you really want to date someone like that?
As for your latest exes, it's sad but true. There are a lot of theories on why girls end up in abusive relationships. My theory is that it frequently comes down to self-worth. Most girls (in the US at least) don't seem to be raised to stand up for themselves, believe that they must look like the latest toothpick fashion models to qualify as beautiful (and if you're not, then you're worth less as a woman, no matter your other talents), and so forth. So girls end up feeling like they don't deserve something good (like a nice, sweet guy for a bf) because you have to *be* wonderful to have someone wonderful be in love with you. They end up in abusive relationships because they don't feel they deserve anything better, because after you've been in one (or several) it becomes familiar (i.e. habit) and while bad, familiar is comfortable (and thus preferable) compared to something new (and scary) that makes you question if you really deserve all this wonderful stuff (like a fun, sweet bf). There are other reasons, but I've seen this one waaaaay too much.
And is there hope for love for geeks and gamers? Absolutely. I met my husband in a Subway Sandwiches. He was the only one on shift. I went in to get a sandwich, which I ate inside because it was cold out, and shared it with my lovebird. I was 2 weeks out of a bad relationship, and guys were no more than other breathing beings to me. He asked how my sandwich was when I brought the tray back to the counter, and was soon talking to my bird. That was almost 17 years ago...