My advice is to do one (or both) of these two things:
1. Attend a local IGDA chapter meeting. Ask your buddies if there is a meeting coming up. If there isn't, find out who runs the local IGDA chapter and say you've been waiting with baited breath for the next meeting (a little flatter never huts).
2. Simply write a very clean, short, and sweet letter or email to someone at the company asking for an informational interview. An informational interview is a meet-and-greet kind of chat either on the phone or in person (or IM, I suppose) that lets you ask questions like, "How did you get hired here? What's it like to work at this company?" Many many people will be happy to do an informational interview, especially if you approach them in the "right" manner (which is totally subjective, unfortunately).
Or if you already know people who work there, why not try and have that person arrange a happy hour where you're invited as well? That way you can meet the people who work in the company, find out more about what it's like there, and gauge what kind of openings they might have.
Remember, if a company isn't hiring a position you fit, you just have to look elsewhere. There's nothing a company can do if they just have no need for your particular skills. But meeting people and letting them know who you are and what you do gives THEM an advantage when it comes time to fill a space that DOES meet your skills. If they know you're interested and fit the bill, they might just interview you before even posting the job.
Does that help?