Can't read any sim card

Hello, I tested an old iPhone 4 and it seems to be faulty, because it can't recognize any sim card. I tryed around 4 sim cards from different providers but no chance.

If I should type in the sim card pin, the phone stucks. If I restart the phone (home + power button) it boots in the homescreen and the sim card is unlocked but the iPhone can't find any connection. This method works only sometimes.

iOS 7 is installed and I tryed 2 times the factory reset without success.

I suspect, the sim reader is faulty, I'm right?