migrated using the application migration service instance can't start

You don't mention what the underlying operating system is. Make sure that the operating system is supported by the Application MIgration Service Supported O/S. You can also try to create another network interface and attach it to the instance. Also, verify the security group allows the traffic that you are expecting.

Version of OS is Ubuntu 21.04, and instance sucesfully migrated to AWS, but fails one of two status checks. We created new security group with allow access. We do not see an error log to determine why the check does not complete. How we can see the logs?

I added another additional network interface, but this unfortunately did not help, still 1 of the two checks passed