As a first step, you may need to re-seat the connector cable of the [http://gsmserver.com/nfs/product/846050/image/500/SIM-Card-Connector-for-Samsung-I9190-Galaxy-S4-mini-I9192-Galaxy-S4-Mini-Duos-I9195-Galaxy-S4-mini-Cell-Phones-memory-card-connector-with-flat-cable.jpg|SIM tray] to the board.
If your are not sure which one it is, take the phone apart, examine every cable/connector on the board and/or just re-seat them all.
If you know which one it is, try also cleaning that connector with a cotton swab and 90%+ isopropyl alcohol (rubbing alcohol).
If the phone works with a different SIM (or as a precautionary step), clean the contact points of your original SIM card with an eraser or isopropyl alcohol. May be it collected something from your fingers during disassembly.