I just reactivated my phone plane yesterday, and my phone seems to not respond to the network, or tracphone.

call tracphone or other carriers. This phone may not work on 3g which has limited time remaining.

Did you have a lapse in service?
Did you just add airtime after lapse in service?
You have added time but your sim card is not active, which is what Tracphone does when you have lapse in service.
You need to talk with their customer service reps who will help you get your phone up and running again.
Customer Support FAQ TracFoneWireless

Here you go this is not my video but i did a search on youtube for you. This should work for you.

Tracphone
Check the phone settings before you connect to Cell network.
eg. Airplane mode. Smartphones start communicating right away when you connect which will eat into your $$$$.
Turn off Internet comms till you track down whats using $$

dial 611 on your tracphone to get customer support.

Click on this URL. It will take you to the TracFone Activation and Reactivation page. Just answer the questions. You can activate your phone online. Click on the link below.
https://www.tracfone.com/direct/init_activation.jsp?app=TRACFONE&esn=&strEmailId=&clearInit=Y&saidExist=Y&TLJID=&lang=en

I do not have a solution for this problem, but I have exactly the same problem! Is it a common problem for these airplanes?

Service unavailable mean you don't have any network. Check with your service provider if they have barred your service or not. This has nothing to do with mobile phone. If there will be no services from your service provider you will not be able to call or send message or receive calls.

Summary: Check once with your mobile service provider.