HI,
ok, I think the problem is that your representation of the object should not be the actual reference in your system.
you need to maintain a reference in your game, and when the user is picking an object, store this reference instead of the visual representaiton of it ( the gameObject lying on the floor).
Then if you delete the object, no problem, it was just a visual representation of it.
But as is it's difficult to give you more details, since I am not sure what kind of data you want to convey when picking an object or playing an object.
bye,
Jean