The second sounds like you are denying what someone has just said. "Jane tried to contact Tarzan." "No, she didn't." "Yes, there an attempt by Jane to contact Tarzan." "I'm telling you, there has been no attempt by Jane to contact Tarzan."
There is a subtle difference actually. The first instance implies that Jane has not made any of several (implied plural)possible attempts to contact Tarzan. The second implies that Jane has not made any one (implied singular), or specific , attempt to contact Tarzan.