I hade the same problem with my VW Passat mate rotten luck it is i had it since november i had something about that i'll find it and tell you keep looking you might get lucky.
I think the system on the Picasso incorporates a diagnostic self test but a code reader is needed.
When you say "the fuses seem o.k. have you tested them with a circuit tester ?
Have you got the Haynes Manual for reference. ?
Have you checked that the pollen filter is not blocked ? If you have checked the filter and fuses it could be the air con.relay,it could be a few things, so I would go for a readout to point me in the right direction and save a lot of time, guess work and money.Best of luck.