Can you confirm that the phone reads the sim card properly?
It sounds like the phone is rebooting on sim insert because the sim detection pin (basically a spring mechanism in the sim reader) gets triggered and tells the phone the sim tray / sim card has been inserted.
If it says no sim card detected on the lock screen or in the status bar (notification bar menu) the sim card is not being read due to either the sim reader being damaged or the phone having a no baseband or no IMEI issue.
To ensure the sim card is being detected go into phone settings > more > mobile networks
On that page it should display only the network settings for your service provider (the sim card you inserted) if it's blank then it's not reading the sim properly. Try doing a call as well, it will tell you to insert sim card if it has not detected one.
You can check imei (15-digit number) and baseband (version) under phone settings > about phone > phone status / phone info.