So, again with some troubleshooting. I think this should be by now an old topic, however, just thought to mention it here in case you are new and not sure what to do.
The errors message your getting is "A service specific error occurred: 90." and "The Microsoft Dynamics AX Object Server service could not be started." - I am not sure if the error is shown like this when you start the service from the Services MMC, so you'd better try from a command prompt with the faithful net start aos60$01.
Simply put, what this means is that the SQL Server you have in your AOS setup is not reachable, or, the specified domain credentials you used when setting up the AX AOS service does not have login privileges to SQL Server at all or to the AX's databases.
So, to fix this check all of the following and correct the incorrect one:
1. open the AX 2012 Server Configuration utility and check that the SQL Server and the Database are the proper ones;
2. login to SQL Server and check that you have for the AOS account a Security \ Login object created;
3. the AOS account must be a user in the database and must be assigned to the following database roles:
In addition, the AOS user must have the following user rights and permissions to execute stored procedures in the database:
(of course on item #3, I always take the shortcut in DEV and assign also the db_owner role to the account, thus not having to grant the execute permissions on the stored procedures).
Details on item #3 can be found at https://technet.microsoft.com/en-US/library/ee355053%28v=ax.50%29.aspx.