In a cognitive radio scenario we consider a single secondary user (SU) accessing a multi-channel system. The SU senses the channels sequentially to detect if a primary user (PU) is occupying the channels, and stops its search to access a channel if it offers a significantly high throughput. The optimal stopping rule and power control problem is considered. The problem is formulated as a SU's throughput-maximization problem under a power, interference and packet delay constraints. We first show the effect of the optimal stopping rule on the packet delay, then solve this optimization problem for both the overlay system where the SU transmits only at the spectrum holes as well as the underlay system where tolerable interference (or tolerable collision probability) is allowed. We provide closed-form expressions for the optimal stopping rule, and show that the optimal power control strategy for this multi-channel problem is a modified water-filling approach. We extend the work to multiple SU scenario and show that when the number of SUs is large the complexity of the solution becomes smaller than that of the single SU case. We discuss the application of this problem in typical networks where packets arrive simultaneously and have the same departure deadline. We further propose an online adaptation policy to the optimal stopping rule that meets the packets' hard-deadline constraint and, at the same time, gives higher throughput than the offline policy.