I don't know about our 'newer' aircon, but the compressor on my '78 engaged regardless of if the fan was turned on. i.e. They were separate circuits. So turning the aircon switch on, still engaged the compressor, and it was your choice if to turn the fan on or not. I just looked in the Volvo aircon manual I have, and there's no electrical circuit in it!?
If the car was in front of me, I could probably work it out in 20 minutes. But plugging in wires isn't the best way of fault finding. ;-)
The circuit should be fairly easy to fault-find, even without much electrical knowledge...
Check the fuse. e.g. If there is anything else on the same fuse, is that other thing working?
Then at the rear of the snowflake switch, with key off, check any ground wire is actually grounded (multimeter on beep/continuity setting, remove the wire you think is ground from the switch, stick one probe in that wire, the other to metal on the car). If it beeps, ground is ok - replace.
Then start following the other wire - check its connections. When you reach a relay, check it's ground wire/s the same way. You could also test the relay itself using a site explaining simple relay tests - like:
http://www.wikihow.com/Test-a-Relay
And going through what I typed before. Sorry, trying to help, but it's hard without the car in front of you. (Remember there won't be any voltage at the relay unless the engine is running, and revs are brought up a little.)
In short, you're looking for a broken connection (blown fuse, open ground, no voltage), or a short circuit (a connection that should not exist), or a faulty relay.
