Strange Electrical Issue

[AF59]

Hi there, I'm new here, so please advise me if I am in the wrong place. I am hoping that with all the expertise out there, someone can come up with a solution to a strange electrical issue I have with my wife's car, 2002 Mk 4/5 Fiesta Freestyle 1.25. 

Once the car has been started, neither the indicators, heater fan, or electric windows work for a few minutes; at the same time, the lamp in the air- recirculation switch is glowing dimly at the same time, although if you operate the switch i.e. switch on air recirculation, it glows with normal brightness. To me, this indicates that power is feeding back through the switch - obviously something it is not supposed to do. Once a certain amount of time has elapsed, the lamp goes out, and the other circuits are live once again. I have checked the common earth point at the base of the drivers' 'A' Pillar, and had to replace one of the ignition relays in the fuse board on the drivers' side, as it was showing heat damage. I have also had to replace the heater control valve. This problem only started when I had to replace the battery a few months ago, and it is worse when the weather is cold and damp.

I have had the battery analysed, including load testing, and checked the voltage across the battery both without and with the engine running - 12 to 12.1V without, 14.26V to 14.4V with respectively. The engine turns over perfectly, firing up straight away; I just have to wait anywhere between 3 and 10 minutes before these circuits start to function. Although I stated earlier that the issue was worse when it was cold and damp, there has been little change over the course of this warm bank-holiday weekend. It is extremely frustrating, and potentially dangerous if you forget to wait!
PLEASE CAN SOMEONE HELP! Many thanks.

[MarksST]

Can you check the fusebox for signs of damp or corrosion.

[pragmatix]

Clean the fuse box under the bonnet, and not just the fuses but also the underneath, damp and corrosion is often the cause of problems like this.