Well, are you familiar with what's under the hood in your car? Do you know how engines work in general?
I can't tell from your diagram, nor do I remember specifically what options are in the car you mention, but you should check the following: air conditioning, power steering, alternator (you say no), water pump/cooling system. It's hard to diagnose a problem without being able to physically look at what you're talking about.
Anyway, what basically happens when your car is running is that the gas you buy goes into the pistons. They are combined with the corresponding ratio of oxygen (from the atmosphere filtered through your air filter). Each piston fires in a specific timing (which becomes important later) in order to propel the driveshaft (creating torque). The torque from the driveshaft goes into your transmission, separated by a clutch (pedal if standard, internal to the auto transmission), then the transmission gears for power (low gear + high rev) or speed (high gear + low rev) and sends the energy to the wheels to spin.
Now, the direct current that the engine generates is converted into alternating current by the alternator. Electrical systems require an alternating current to operate, so all your car's electronics are wired to the battery which is wired to the alternator. Now, in order to keep your engine properly timed, there is a belt attached to your engine. That belt must be attached to most of the other mechanical systems in your car in order to provide them power/energy.
Keep in mind that this is GENERALLY how cars are constructed. Some models have separate belts for different systems (it isn't necessary that every mechanical system be attached to the timing belt, so perhaps that's on a separate belt system).
All that being said: search google for an engine schematic for your make and model. They may have a diagram online that tells you what is what. Check a mazda car owner forum and search for similar problems. The pulley could be not moving because of something simple like a spot of rust, or debris stuck in the system, OR, it could be symptomatic of the entire mechanical system it's attached to failing to function. Since the mechanics can't function, the pulley can't turn because the pressure in the system is greater than the force of the belt attempting to move the pulley (and thusly the whole system).
So where does this leave you? Well, you can spend hours painstakingly diagnosing the problem, OR, if you're sure that it's THAT pulley that's the offender, you can simply replace the part on your own. Do yourself a favor and head down to your local AutoZone (or equivalent auto parts retailer). They LOVE answering questions and have all the literature for the mechanical repair of pretty much ANY car part. Take some pictures, or just drive your car over there and ask if they can take a look and advise you. They're there to help save you some money with DIY advice, etc.
Good luck.