Could a faulty paper sensor be the cause of the persistent 'Out of Paper' error on my HP Deskjet 2600, and how can I diagnose it?

Yes, a faulty paper sensor is a possible cause. Diagnosing it is difficult without specialized tools. If you've tried all other troubleshooting steps (clearing jams, cleaning rollers, checking settings, updating drivers) and the error persists, the sensor is a likely culprit. This usually requires professional repair or replacement of the sensor by a qualified technician.