Hi,
Did you mean to add the domain account under Computer management as below?
If so, the domain account should have the permission to access the files of which Admin has full control.
Would you please let me know what files your domain account fail to access? Please help to list some.
Also, I suggest you use the Process Monitor to capture the system event when you repro this issue.
Process Monitor v3.05
http://technet.microsoft.com/en-us/sysinternals/bb896645.aspx
You can also try to use this article to troubleshoot this issue.
Solving Access Denied Errors Using Process Monitor
http://improve.dk/solving-access-denied-errors-using-process-monitor/
If there is any difficulties, please upload the saved pml file from this tool here for our research.