There could be a number of things that are going wrong with your node setup and render layer setup.
I will make some assumptions here:

• You have your scene elements organised on appropriate layers matching your render layer set up.
• Under the "Render" tab you have "Transparent" checked in the "Film" section for the scene elements that you want to composite.
• In the attached picture you have the highlighted areas under the "Check" text selected in the Node Editor.
• The "Backdrop" image you mentioned is a separate image.

The attached image shows a basic node setup to composite an "object" render layer with a "shadow" render layer on a separate background image.
To add your viewer node press "Shift+A" and select it from the Output options.

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