Hello, I hope I can offer you some assistance.
Flash code 16 is either incorrect key been used which we can disregard as you've tried 2 keys or a Controller Area Network (CAN) communication fault between the engine management and the instrument cluster.
Check fuse 30 (3amp) in the fuse box next to the battery, this fuse is for the engine management control module and as it is only 3 amp blows easily giving the symptoms you have. Also check the fuses in the fuse box below the glove box.
If all these are OK then unfortunately you need to have the fault codes read from the engine management and instrument cluster to pinpoint the part of the immobiliser system causing the fault.
There is no master key on this immobiliser system all the keys are the same priority, turning the ignition from position I to II as you describe is to reprogramme the remote locking and has no influence on the immobiliser.
Let me know if I can assist any further or if you have further questions regarding this.