This thesis includes an estimate of the DO silicon detector lifetime as well as two measurements of the top quark pair production cross section. The thesis is divided into four parts. Part I gives a brief overview of the theory of elementary particle physics, focusing on the top quark. It also introduces the Tevetron accelerator complex and the DO detector. Part II describes the effects of radiation damage in silicon and presents an estimate of the DO silicon tracker lifetime. Part III describes two measurements of the top quark pair production cross section using events in the dilepton final states. The last part of the thesis, Part IV, contains a summary and outlook, followed by an informal summary in Swedish.