I can make calls, but I can not recieve them

Hi.

Problem description - My iPhone 5 can make calls, but when other people call me, it rings on their end, but it doesn't ring on my phone. It doesn't even show them as missed calls. So nothing. The caller thinks its ringing and their call is going through, but my iPhone doesn't even make a beep and I am totally unaware. And be assured Don't Disturb is off. I have no problem with texts. I can make them and receive them.

Although I can make calls, but when I hang up the call, it says "call ending". This screen doesn't disappear. I have to restart my phone to get rid of this screen.

Background History - I am pretty sure my problem is a hardware one. I changed my phone battery some time ago, in a local repair shop. The new battery was working splendidly when out of a sudden the phone just turned off. I was shaking it when that happened. So I thought the battery was just loosened due to the shaking. I resent it to repair shop again. Although the old problem was fixed, this new problem has surfaced. I haven't restored my phone, I don't think it will solve the problem.

PS: The phone can not find the service provider and displays "searching...". It can only find it when I reset my phone.

Do you have any Idea how to solve the problem? Will it be solved if I change the SIM card IC? and Please provide instructions.

Thanks in advance.