Dead Fret

Have you tried changing strings on it yet?
Can you post a photo of what the tuning machine's capstan looks like, and maybe with a little bit of the area where the string crosses the nut?

 

Dead meaning less sustain on the low G or dead meaning no sound at all?

 

If you tune down half a step does the deadness move down one fret?

 

Give it a decent burial.

 

I too would first look at the string. A dead spot in that particular location is highly unusual.

 

As the others have said, the most likely cause is a worn spot on the string. But, if it isn't that, it could indeed be a dead fret.

A dead fret isn't the same thing as a Dead Spot. A "dead" fret isn't really dead, it's just worn down to a tiny bit lower than the next fret up. When you press down at that fret, the string mutes out on the next fret up. The dead fret is just low enough that the note dies out, but not so low that it rings out at the next fret, a half step up. When they happen, dead frets will usually be on a very frequently played note. You know, like the the 3rd fret on the E. Probably the most used note on a sweet old Fender.

The solution is a quick level and dress of the frets. The offending fret isn't low by much, so it doesn't need replacement or major work. Just a touch up.

 

One other cause of a "dead fret" is that the fret has come unseated. If it is slightly sprung it can cause any notes using that fret to sound dead.