I recently purchased a new desktop computer for my office. Am I entitled to bring the old computer home and use it for private purposes?

The old computer remains CERN property, even if it seems redundant. Ask your hierarchy whether it may be used elsewhere in your group, department or at CERN.  If this is not the case, you may be able to buy it in accordance with the procedure for purchase of obsolete equipment, as described on the Finance and Procurement Department website.