The traditional DNA computing schemes are based on using or simulating DNA-related activity. This is similar to how quantum computers use quantum activities to perform computations. Interestingly, in quantum computing, there is another phenomenon known as computing without computing, when, somewhat surprisingly, the result of the computation appears without invoking the actual quantum processes. In this chapter, we show that similar phenomenon is possible for DNA computing: in addition to the more traditional way of using or simulating DNA activity, we can also use DNA inactivity to solve complex problems. We also show that while DNA computing without computing is almost as powerful as traditional DNA computing, it is actually somewhat less powerful. As a side effect of this result, we also show that, in general, security is somewhat more difficult to maintain than privacy, and data storage is more difficult than data transmission.