Make it a habit to copy the background as the first thing you do (drag the background layer to the new layer button). That way you've always got the original, and can work on the copy.
The first time I did something similar, the new layer was locked too, but I was using ctrl-j to make the copy. Have just tried your suggestion of dragging to the new layer button, and that seems to work OK.
I have an old version of photoshop so this might not work... ...but if you double click on the background layer i get a 'make layer' dialogue opening that allows you to change it into a 'full' layer.