My car Toyota Corolla 2008 starting problem

What is your question?

My car has starting problem since 4 month before three months problem coming twice in a month but now coming every 2 days and if car started then no problem you can start stop many times that day then no starting problem only first time starting problem car taking long self untill you press the key but not started I check battery starter is good their is no engine check in light but car not started I checked with computer also their is no fault code but when starting problem that time I try maybe more then 10 times then it's got started but some times it's started after 2 days crank sensor also replace ,plug also good engine oil change before 1 month 2 times computer reprogrammed but still same starting problem some mechanic told key immoblizer problem but when I inserting key security light got off and blinking untill I remove the key but when it's started then it's running normal.please give me suggestions what I need to do What seems to make the problem better or worse? When the engine is cold or I stop my car at night then I started morning but not started but sometimes with first self started.sometimes morning I started but evening not started How long have you had this problem? 4 month