Hi TxCelt -
Csaba is correct. If you do not edit your group, anything that you draw will actually be on top of the group and not affect its surface planes.
It's difficult at first to notice that you have a group selected when the geometric object is a rectangle, because the group (and component) bounding box is also a rectangular shaped cube. To illustrate this more clearly, create a circle, then use the Push/Pull tool to create a cylinder. Now make that a group (or component). You'll now see that the group object will have a rectangular bounding box when you select it. Now double click on this object and you'll see that you are now editing INSIDE the group.
This is what you'll want to do with your plywood group objects.
One other note: components are similar to groups, but have a more powerful feature. When you create a component, and then copy that component a number of times within you model, editing any one of the components will affect all of the other instances in the same way. This is very powerful if you are modifying a number of repeating objects because you don't have to edit each one individually. If however, you would like to edit a component and not affect the other instances, you can right-click on the component and select "Make Unique". This will break the link to the other instances and allow you to edit it without causing the others to change.
I hope you find this information useful, and you share with us your successes and questions as you go! And thanks for using SketchUp, we hope you enjoy it!!
Cheers,
CraigD