We consider the distributed uplink resource allocation problem in a multi-carrier wireless network with multiple access points (APs). Each mobile user can optimize its own transmission rate by selecting a suitable AP and by controlling its transmit power. Our objective is to devise suitable algorithms by which mobile users can jointly perform these tasks in a distributed manner. Our approach relies on a game theoretic formulation of the joint power control and AP selection problem. In the proposed game, each user is a player with an associated strategy containing a discrete variable (the AP selection decision) and a continuous vector (the power allocation among multiple channels). We provide characterizations of the Nash Equilibrium of the proposed game. We present a novel algorithm named Joint Access Point Selection and Power Allocation (JASPA) and its various extensions (with different update schedules) that allow the users to efficiently optimize their rates. Finally, we study the properties of the proposed algorithms as well as their performance via extensive simulations.