Your skills sound marketable to me. So I would be inclined to ask whether by "programming skills" you meant something more specific, like desktop application programming skills or skills at writing algorithms? Last time I checked inordinate amounts of websites are using SQL (typically but not always MySQL) and either ASP or PHP, so I would be hard-pressed to think web-programming skills are not marketable or in demand, or that you haven't gained considerable domain knowledge from your years of experience.
Consider opportunities where you are. You could certainly have a conversation with your boss and convey your aspirations, and let him or her know how s/he could help you reach some of your domain expertise goals. Granted, business concerns may come first, and you may not be able to only work 100% on your favorite part of the job, but when your boss is trying to decide whether you should do X and Joe, your coworker should do Y, or vice versa, if s/he knows what you would like to be doing, it may help sway the decision making process to align your assignments with your interests.
Decide what you would like to specialize in. If you feel like your current position is pigeon-holing you into a specialty you're not interested in continuing longer term, start by evaluating what other specialty you'd prefer to pursue. Considering what languages are popular in your area, or what languages and skills are in demand on job listings may help narrow down the list of choices. Would you rather be a C# programmer? A PHP programmer? Learn Java or C++? Become a database guru? Etc.
Build skills in your desired specialty. Once you've picked an area you'd like to focus on, you should find a way to build up those skills. If your boss isn't interested in using those languages in-house, you may want to consider a project outside of work. It doesn't need to be a demanding project, but something to get that other language back fresh in your mind. Perhaps you could join and contribute to an open-source project. That's a great way to get your foot in the door to working with a new or different technology, with the added benefit that your source code there isn't proprietary, so you can use in in a portfolio for future employers. You could also consider joining a professional development group for people who are interested in the technology you're interested in, if there is one in your area. Or even just start reading a couple books on it, or look for university extension classes for professionals where they teach that language to brush up on it.
Sell your experience for all its worth. In the end, what you're looking to show is that, even though you don't, for example, have 3 years experience programming C#, your new desired career direction, that you have seven years of experience programming in other languages where you have learned all kinds of transferable skills (abstracting and breaking down problems, maintenance of existing code, working with teams, learning new/different technologies etc etc etc), plus you've recently been tackling learning this awesome new skill that's what they're looking for, which makes you a much more awesome candidate overall.
Or perhaps, just finding an outlet for skills you don't use at work would be enough to feel fulfilled. That's your call.