This solution picture below shows the connection line paths of the SIM card pin connector which tells us where and what components on the PCB board needs to check.
Nokia 3720 classic insert sim
Nokia 3720c insert sim card problem repair hints:
1. Ensure that the SIM card you are using is 100% working.
2. Clean the SIM card slot pin connectors.
3. Check and trace the SIM card supply voltage (VSIM). When the sim card inserted, you can check around 1.3V to 2.8V. The voltage reading varies according to the type of the SIM card inserted.
4. Check/replace the VSIM filter coil.
5. Trace the SIM Reset pin and Ground pin connections.
If the above procedures won't work and or the VSIM voltage is missing, The possible faulty is the AVILMA IC.
6. Try to re-heat or re-hot the AVILMA power IC, then rework or replace if necessary.