What is the most important strength that you have? Think about this very carefully for a few seconds.
And here is the answer. The most important strength that you have is... YOUR AGE. You have all the time in the world to get better at anything you want to. Employers know this, but you don't. Why? Because young people don't consider youth as an asset. However, youth is the most important asset in the world. With time you can do anything. If you don't have time, you can't do shit.
Why is this important? Think about Warren Buffett. His first serious job was working for Graham for FREE. Why did he do it for FREE? (actually, virtually free). Because he knew he was in the right place to learn and become a good financial analyst. He realized that he had all the time in the world to make money. He could have gone work with other people and make more money in the short term... but the long term is a different story.
Contrary to what somebody said here, this is NOT a critical decision in your life. As a matter of fact, I hope that you make many wrong decisions NOW, because the more you fail NOW, the smarter you'll become. There is no such thing as a wrong decision when you are in your 20s. They are simply invaluable learning experiences. When you turn to 30s, or 40s, or 50s, then and only then it is when you can't afford a mistake. Until then, by all means, make decisions, as carefully as possible, but don't worry too much about failure. To try and fail is always better than fail to try.
Let's apply this framework to your situation and forget about the money and Salary.com. Think about the big picture. Think about the forest and not the trees. Where would you be able to learn more? In your current shitty paying job or in the big company? Where do you think you could grow faster as a person and as a professional? Where would you have more responsibilities, more EXPOSURE AND VISIBILITY? I know of many smart people who work in cubicles in big corporations and have no visibility whatsoever. The result? They are stuck in the same position they were 5 years ago.
As for the money, well, how old are you? How many projects have you completed that could justify a, say, $45K salary or more? These are just questions that your employer probably has considered. How many other serious offers do you have?
And now, my suggestions:
1- You could tell your boss that you'll take the job but you want a performance review in 3 months (meaning a salary review).
2- You could tell your boss you'll take the job but you want an incentive plan based on specific milestones. This is a win-win. The more successful projects you complete, the more you get paid.
3- You could always take the job, maybe agree with your boss to work less hours (who says you need to be in the office 40 hours to meet all deadlines?) and keep looking for another one! Forget about ethics for gods sake. You have to take care of yourself. Nobody in the world is going to take care of you but YOU!
However, if you do take the job, whining, bitching and complaining is not allowed. You take it and you give your best and don't use your low salary as an excuse for poor performance.
Also, honesty with your boss is critical. He has probably dealt with many many people like you before so he is more experienced in these situations than you. I would explain to him exactly how you feel, in a candid and straight forward way. No drama, no emotions. If he is reasonable, he will understand how you feel. If he doesn't, that's a red flag for me.
Finally, web design is a tough industry... unless you have some really cool projects to show off. It can easily be outsourced to other countries. This could be an opportunity for you to lead some projects, make a name for yourself, and then ask for more money to this boss or the next one. But first you need a portfolio of really good projects (you may have it already, I don't know).
I wish you all the best, and keep us updated. I'd like to know what happens with this :)
Take care and good luck.