Okay coming to the solution. Use the second key, if the issue is resolved the issue is with the first key immobilizer. Get the first key fixed. If the issue isn't solved with the second key too, first check the second keys battery, if issue still continues get the car scanned maybe any issue shows up. Another issue might be with the cars immobilizer system. Just open the under panel of the steering wheel(usually held by clips) and check for any disconnected wires. If the issue still isn't is fixed, get it checked from Suzuki, don't let any local mechanic open the immobilizer System. Most of the times the mechanics just say , the system is faulty and ask a heavy amount to fix it without confirming if it will be fixed.