Can you tell me what is wrong with my phone and/or how to fix it?

I have a Samsung phone with AT&T as my provider. Within the past two days, I’ve been having a few problems with my phone. Intermittently, the phone with just stop working, in the sense that it will neither send nor receive calls or text messages. All the bars of signal are there, but occasionally the “AT&T” logo at the bottom of my display will disappear. Sometimes, when I attempt to make a call, the display will tell me it’s dialing, but will never connect. Other times, it will tell me that service is unavailable or that I can only make emergency calls. With text messages, I will try multiple times to send one, but it will ask me if I want to try again. If someone calls my phone, it will not ring, but the caller will hear two rings followed by my voicemail message. Once it decides to work, I usually get a bunch of texts and voicemails at once. Today, I managed to have a conversations for a little over a half hour, but the call dropped, and I wasn’t able to connect again. I have tried turning my phone off and on many, many times, I have tried taking out my battery and taking out my SIM card, and I have charged the phone fully. I have left it off for periods of longer than twenty minutes.