My guess is that the Logic Board is not seated correctly at top of iPhone.
No SIM means that there is no SIM in the Tray, or that no SIM is detected in the Tray, or that the SIM Tray is not pushed in all the way. No Service means that a SIM is in the Tray is being read, but it cannot get Cell Service for whatever reason, usually very poor reception, ie poor signal from carrier. But since you are have SIM Tray problems it might not be getting reception due to problems in the SIM Bay (SIM area). My guess is that the Logic Board is not seated correctly at the top of the iPhone so that the SIM Tray is not ending up exactly centered over the SIM Bay 6 Gold Reading Pins (SIM Junctor).