Even without the remote on the dock, the charger lights should glow faintly - turn out the lights and check this.

If they don't glow, it's either the wall transformer that's bad (less likely) or the dock.

If the wall transformer is warm to the touch when it's been plugged in a while, it's most likely OK. If it's the dock itself that's bad - the most common problem is the internal, solid state fuze is blown. You can do a forum search for more info (lots of threads on the fuze) and either repair it yourself or take it to an electronics repair shop.