In the network activation problem, each edge in a graph is associated with an activation function, that decides whether the edge is activated from node-weights assigned to its end-nodes. The feasible solutions of the problem are the node-weights such that the activated edges form graphs of required connectivity, and the objective is to find a feasible solution minimizing its total weight. In this paper, we consider a prize-collecting version of the network activation problem, and present first non- trivial approximation algorithms. Our algorithms are based on a new LP relaxation of the problem. They round optimal solutions for the relaxation by repeatedly computing node-weights activating subgraphs called spiders, which are known to be useful for approximating the network activation problem.