Ages ago in a now defunct e-mail forum I asked a similar question and have seen this come up time and again.
From what I've learned and what I can recall the LME should be fine to use. My question was related to a 10 year old can that was bulging. I did use it, it made beer just fine. Over time the LME will darken, so you'd want to go with a darker beer. The brix (sugar content) should keep it from developing botulism (a big concern that was raised in that old discussion).
I believe John Blichmann (it may have been someone else) ran some side by side experiments with old LME and it all fermented fine. My recollection was that you should use a greater amount of yeast than normal to get it to ferment without getting some older, carmel-ly flavors unless that's what you're looking for.
I didn't get any off flavors, but it was a very dark malty beer.
The DME is likely the same story. I would imagine it is much like old brown sugar (hard as a brick) which is fine to use.
The grains I would assume are stale... But who knows? Taste and smell would give a good indication.