Okay, I'll weigh in...
In years past, I earned a good portion of my uni tuition repairing automobiles, and often worked with timing and accessory drive belts. What you describe would be typical of a slightly misaligned Gilmer belt (
http://en.wikipedia.org/wiki/Gilmer_belt ), which is the type used to transmit drive power on your belt-equipped Rohloff.
It doesn't take much misalignment to result in a chirping or squeaking sound. I suspect your eccentric bottom bracket may have shifted sideways a slight amount, accounting for the noise when pedaling. Gilmer belts are often joined diagonally in a seam, and this can produce a slightly stiffer spot and that's usually where any noise will arise if the pulleys are misaligned. That's where I'd start. You may well have to replace the belt after realigning the eccentric bb, but I'd try an adjustment first. The noise is reduced when wet because water is acting as a lubricant on the belt, reducing friction where the seam goes 'round.
If you have access to a mechanic's stethoscope, that would narrow the hunt immediately. I have a couple, and often use them when I am trying to find, isolate, and eliminate a noise in motorized or mechanically-actuated parts. Leads one right to the source. If you don't have one, you can make a reasonable but crude substitute by placing the tip of a screwdriver against the bearing housing of the item in question, then resting the screwdriver handle against your temporomandibular joint (sideburn area, just ahead of the ear). This will transmit sound by bone conduction. After making sure hair and clothing is well out of the way, slowly turn the crank with the bike in a stand, and you'll hear all sorts of disturbing sounds. The one you're looking for will likely come once each revolution. This method does work, but will draw the odd comment from passersby, each of whom will make the same unoriginal remarks about loose screws.
Noise isolation and identification on a bicycle is notoriously difficult to locate and resolve, owing to the way sound telegraphs from its original source. What sounds like a noisy bottom bracket can sometimes originate as a loose saddle frame, for example.
Best of luck!
Dan.
