The INSERT/UPDATE/DELETE permission was denied on the object 'TheTable', database 'TheDb', schema 'dbo'
Try with the below script. Its works for me.

GRANT SELECT ,UPDATE,DELETE,INSERT ON OBJECT::YourTable  
    TO [Domain\User];  
GO   


I tried to the mentioned permission to a user Anoop,in the database MyLab.

GRANT SELECT ,UPDATE,DELETE,INSERT ON OBJECT::Account  
    TO [*MyDomain*\anoop];  
GO   


And below is the screen shot after giving the permission.