Stock market confusion?

I have a very limited understanding of the stock market, so bear with me. My question is this: When people sell and buy stocks, does the company profit at all? The company gets money when the first stocks are sold, and then after that people buy and sell the stocks. But the company doesn't get any more money from the buying and selling of stocks, does it? The company has already gotten its money from you, so how exactly does the value of the stock go up? I hope you all understand my question!

When a company 1st goes public (IPO= initial public offer), then it does get proceeds of how much the stock sells for in the opening offer, but after that, the company has no direct gains from the price of there stock (if they still own a buch of there own stock, they can sell it later on for the market price & if the stock goes up they would make some profit/ but they must make an announcmet of this b4 had) same thing when they are buying it, say they think there stock is way too cheap & they know there company will make lots of profit, so the company may announce a stock buy back and then sell it whn the price is higher, therefore makeing some $$$. Example, Dell stock fell 30% after some ernings report, dell announced a mager stock repurcheace, and dell stock has made some comeback..

Short answer:
No - the company gets nothing.

Longer answer:
The company doesn't get anything directly however the officers of the company typically do get something directly and indirectly by the stock price going up.
1) Their performance is measured "by the street" based on the stock price. If you have great fundamentals but somehow your stock price is still going down chances are you'l be out of a job soon.
2) A big part of their pay is in "stock options". These are just what they sound like - the option to buy stock. The kicker is it is typically at a set price that would earn them a profit if they turned around and sold it. Even better if they don't "exercise the option" immediately but rather wait a year until the stock price is even higher then "exercise" it they are buying the stock at the original option price meaning that if they turned around and sold it they'd have an even bigger profit.

FYI: Most corporations actually do "buy backs" of their own stocks on occasion to try to help control the amount of shares outstanding and the stock price as a result. These shares do go up or down just like any other stock holders'.