A couple of points about the a/c compressor and the system in general, the ribbed pulley should spin freely with just a finger to spin it, and the a/c switch blue light doesn't indicate if the a/c is working or not - only that the switch is pressed. The a/c compressor clutch is triggered off a relay, but it should be off without power or most definitely with the fan & a/c turned off. There is the faintest chance that the relay has stuck closed keeping the a/c compressor clutch engaged but you can eliminate this possibility by pulling out the relay from the under bonnet fusebox. All the relays are the same so you can swap them around and use the horn relay position as a testbed if you wish.
If the a/c had run out of gas/oil then the compressor could well of died, but there is a pressure switch right next to it that should isolate it when the pressure gets too low. You can reach both items through the drivers side (RHD) wheel arch by removing the liner, when the a/c has gas the pressure switch is closed and open circuit when the gas has escaped.
I have read of repairing the a/c compressor clutch but that seems like a lot of effort. Swapping in a breakers yard compressor is probably a good idea, but getting the a/c recommissioned might be a waste of money - it's £50 for the gas/oil to be recharged, and there may be a leak or fault elsewhere in the system. You
should get this done by a licensed a/c specialist who can recover any remaing gas in order to protect the environment, but if there is no gas in it to start with then it may be a different mater....
http://www.ebay.co.uk/sch/i.html?_nkw=honda+jazz+compressor £30 posted
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TG
