Mobile network not available on unlocked Active
First, make sure the APN settings on your phone are correct for your carrier. Next, try cleaning the SIM card's and phone's contacts. You should also try a different SIM to rule out a broken card (also try your current SIM in a different phone.)

If the problem persists - then it's most likely a hardware issue with the phone's SIM card connector.  You may want to get in touch with Samsung to send the phone in for service.

The SIM card contacts on the phones are notoriously fragile, and can be easily damaged by using an adapter (Micro-to-Nano for example) that is either defective or simply improperly manufactured. If the adapter is not an exact fit, the contacts can get "caught" in the gap and bend or even break off during removal.  It's possible this is what happened to the previous owner of your Galaxy S4.

This type of damage is usually not covered by manufacturer's warranty, but it won't hurt to try anyway.  Worst case - there are SIM housing kits available for sale for the Galaxy S4, and ste-by-step replacement instructions on YouTube.  It's fairly easy to replace this module on your own.