I agree with the advice Schmange gave in regard to checking your pick-ups as well. If the coils wound into your pick-ups become free to vibrate, a noise results. That noise runs through your amp and out it's speakers. The resulting soundwaves interact with your pick-up. Potted pick-ups can lose their effectiveness as the wax can deteriorate over time, even the covers can lose that snug fit they originally contained. It's worth checking out.
Good cables are a must for noise reduction as well.

One other thing you could check out is a possible Ground-Loop. Try different Outlets in search for a isolated circuit with a full 120v current needed for most Amps in North America (A lot of recent players have plugged into 120v and fryed their Vintage Amps because in the 60's the US Standard current was 110v and they didn't know the older amp needed to go through a Variac).
A looped circuit is where other componants (like a TV) also draw from the same amperage as your amp draws from and will cause interference.
Isolated Circuits are one of the most important specifications dedicated to the Recording Industry Today.