I have a Sony M4 Aqua, When I turn my phone on the little ticker at the top right of the screen says "No Sim card - No Service". When I swipe the phone it seems to be OK and there is no immediate sign of any problem until I try to use the Internet where there is no WiFi.
"When I turn my phone on the little ticker at the top right of the screen says "No Sim card - No Service"."
Do you mean that you get the above message when the phone is powered on from cold? Does the message persist or does it go away after a few seconds? If persistent it could mean the SIM has dirty contacts, the firmware in the phone needs to be updated, the SIM slot is faulty, or (very rarely) that the SIM card itself is faulty.
Or do you see the message when the phone is woken from standby?
If testing another SIM in your phone, try to use one that is not EE related. So a Three, Vodafone or O2. Free Three PAYG SIMS can be easily ordered from their website here. You don't need to add credit to use it. Put the SIM in the phone, power it on and wait a few minutes. Action any SMS texts you receive concerning network settings. Then call the Three number from any other phone. It should ring and shows that everything is OK. Obviously you can't test mobile data without credit.
Assuming your Virgin SIM is OK and your M4 is OK it might be down to a signal strength issue and the handset hunting for a stronger signal.
So goto Settings > More > Mobile Networks > Preferred network type. Note the mode currently set. Don't use any 4G mode as Virgin does not support 4G at all except on certain business tariffs. Try 3G only and then 3G preferred/2G. Power the handset off and then on again when changing the mode. You can also try 2G only if you don't need/use high speed data.