The original Sigma DP1 and DP2 (non-Merrill non-Quattro) are cameras that rely on extending lenses. A cable is needed to connect the lens back to the mainboard. A fairly common issue was identified on the Sigma DP1 cameras where this cable would break. This was due to the cable being brittle and repetitive extensions and retractions of the lens. Some users online modified the camera such that the lens extension was permanent using a special cable. There was even discussion of an interchangeable lens mount mod which was later realized on the Sigma Merrill. Unfortunately these threads are now lost from the now defunct Chinese forum http://www.x3-club.com/.
Sigma addressed this in their later DP (Merrill and Quattro) models which do not have extending lenses and focus internally.
From forum browsing, this issue appears to be less common with the Sigma DP2 models. Stating the obvious, when purchasing this camera, make sure that the seller can demonstrate it turns on correctly and is able to take in focus images.
When the camera is off, it is possible to review images without extending the lens. Hold the ⊳ button for 2 seconds and the camera will turn on.