ShowCaption = false;
This is hiding teh caption row, and this necessarily hides teh plus/minus that is part of teh caption row.
The default settings will give most of what you described, so I think you can get what you wanted just setting these properties.
gridGroupingControl1.TableDescriptor.GroupedColumns.Add("Computers");
gridGroupingControl1.TableDescriptor.AllowNew = false;
//this.gridGroupingControl1.Table.ExpandAllGroups();