Mate, there was a time when I was in your shoes, though you'd NEVER know it to talk to me know. There was a time I'd never initiate conversation with someone in a club for love nor money, let alone during the day in an office. As the guys who have been out with me will now tell you though, that's a distant memory these days. I'm constantly on game, chatting to people all day and night. It's just a matter of getting part your insecurities.

It's like door to door sales. When you first start you might need to knock on 200 doors in order to get 5 people excited about what you're selling, but as you do it more and more, you get more natural at promoting the product (in this case yourself). People will throw you negative as to why they don't want your product, and you hear the same things so many times that before you know it your turnaround for that point will be rolling off your tongue. Same thing applies. You need to start talking to people in order to realise that they don't all want you. That's just a fact. No man is wanted by ALL women, but what you're trying to do is sift out the ones that do from the ones that don't.

As you're just beginning your journey of change though, I'll tell you something that I've found works really well in offices.

Regularly (like once a day) go onto a site like www.gorillamask.net. It basically highlights most of the best viral things (videos, pictures, websites etc) that are circulating that day. Watch which links you click though as some are very NSFW (they're well marked as such though).

Find a couple of things that have been going on that day that are interesting / funny / cute (women love things like a cat doing something or that kinda stuff) and just remember them.
Then, if you get a moment when you're talking with a mate and your target is in earshot, mention to your friend (the person you're comfortable talking to) about that thing so that she can over-hear.
Hopefully (as is usually the case), neither of them will have seen it yet, so you can then bring her into the conversation...

It could go a little something like this

You: Did you see that video of the blah blah doing the blah blah. It's so funny.
Friend: No.
You [to girl]: Hey, what about you, did you see it?
Her: No.
You: God, you're missing out. It's hilarious. I'll send you both the link. [then directly to her] Sorry, I don't have your email address. What is it and I'll drop you the link over.

POW. You've probably ended up breaking the ice with her in a completely non-threatening way, and you have her email address in your pocket. Go back to your desk and drop her the email - if she's half decent she'll reply with something along the lines of "hahah, that's funny", or something like that. Even if she doesn't reply, then next times you see her by herself, you already have your opener - "hey blah (assuming her email includes her name), did you get to have a look at the blah blah?" As you've already broken the ice, talking to her a second time should be much easier.
But, if she does reply to your distributed link, then try and casually continue conversation. Be light at first, workplace hook-ups can be volatile (I once hooked up with a girl from work, told her I didn't want anything else, then hooked up with someone else, and the first one went to my desk at night and smashed my monitor - turns out she was crazy though)

All in all, to begin with all you really want to learn is that no everyone is going to be negatively responsive to you - which is probably what you have in your head right now. Speak to enough people, and you'll see that for yourself.

Let us know how your tentative toe-dipping into the wonderful world of PUA goes