No, even if you don't receive the cash, when you sell a stock and buy another, it's treated as a capital gain sale. All of your sale gains and losses are netted as short-term and long-term, with long-term having special lower tax rates.
Stocks you hold that appreciate are not taxed. Holding stock is the only way to defer income. Any sale or trade triggers capital gains and losses (as reported on your year-end statements).
Dividends are always treated as dividend income in the year they are paid, regardless of if you choose to reinvest them. As long as they reported them on form 1099-DIV, it's income because they are excess profit from the company that's paid to you. In other words dividends don't affect your stock basis/investment at all.
If you didn't have a choice to reinvest the dividends and they were stock dividends, the rules get a bit more complicated. Let me know if this applies.
