I had exactly the same problem soon after my husband and I moved into the apartment but fortunately I was born here so I got advice from my family and avoided being ripped off.
OK, first thing, it is the landlord's responsibility to maintain electrical appliances in safe, working conditions (look at your contract for clarity/supportive evidence).
Second, the price you mentioned is actually cheap if saffolding was involved (see below).
Third, if by any chance you have to fix it (again, not your obligation but the landlord's!), google the air conditioner's brand name AND "Hong Kong" and usually there is a section on maintenance and service under which there may be a number you can call to ask about maintenence and repair and/or a list of local companies that are recommended/authorised to repair their products. This is exactly what I did and the price (including scaffloding, which was put up and only put down after about a week after I ran the air conditioning unit for about a week to check it does work following the repair work) was higher than the price you quoted. In any case, my landlord paid (even so, I got the repair company this way so that there is no despute with the landlord in regards to price as it is a contracted local company on the manufacturer's own website...in my case, my landlord asked me to arrange the repair and reimbursed me afterwards as she is rarely in HK).
Lastly, if the above is not valid, then go to your building mangement's office and ask them. For large apartment complexes, the air conditioning units are from the same manufacturer so they must have relationships with them and therefore can point you in the right direction.
Hope this helps.