There were links to documentation for setting up Jenkins to work with TestComplete. Did you follow those?
Also, the solution marked here indicates that the problem was that they needed to have Jenkins run as a local account. have you made that change?
Robert Martin [Hall of Fame] Please consider giving a Kudo if I write good stuff ----
Why automate? I do automated testing because there's only so much a human being can do and remain healthy. Sleep is a requirement. So, while people sleep, automation that I create does what I've described above in order to make sure that nothing gets past the final defense of the testing group. I love good food, good books, good friends, and good fun.