Intermittent Dash Lights + then no Start

Any clues as to what my problem is on my 99 Windstar LX 3.8.

A couple of months ago, all my dash lights became intermittent (might all be off for a while (minutes/hours), then on. Sometimes on/off quickly with a bit of a related chatter sound. All other lights etc seem OK.
Seemed to be worse when it rained.

Yesterday, it appeared that no power was getting to my starter.
.... but there was no typical solenoid click that occurs when a battery is low. Also all interior lights appeared OK.
Got a battery boost... no difference.

I came back hours later and it started no problem.
(But I suspect it will happen again anytime.)

Is there a common electrical module that could be causing these 2 electrical problems?

Thanks in advance,
Mike

STILL WANT AN ANSWER AS TO WHAT MIGHT BE CAUSING ALL MY DASH LIGHTS TO INTERMITTENTLY BE ON/OFF.

Turns out the no-start was a red herring. My wife's key was defective (the anti-theft electronic module had fallen out of the key... leaving a hole in key) and the anti-theft mechanism was causing the no-start.

Mike

I don't know much about the instrument illumination, but maybe this (reading from the diagrams) will help:

The illumination seems to be in two groups:
1. Non-dimmable Light Emitting Diode Backlighting. Used in the power window switches. This circuit has a relay in it -- "delayed accessory relay" in the fuse junction panel -- near drivers left foot. You didn't mention these lamps, but the noise you hear makes me think of relays.
2. The Dimmable Incandescent Backlighting. This seems to be the lamps you're noticing going out. I don't see a relay in this circuit -- just the main light switch "panel" (for dimming action) and the instrument panel itself.

I'm going to hazard a guess that your problem is somewhere near/in the dimming controller.

Thanks.

One thing I did not mention is that it is all lights on the panel, including the turn signal indicators. There is no "clicking" or light to indicate that the turn signal is on.
The turn signals on the outside of the car still work.