99% of Honda aircon problems caused by failed relay ( which if it fails closed can also flatten the battery in a few hours, there was a service bulletin from Honda on Civic aircon relay a few years ago - if it fails to close then compressor will not run ) - other causes are low gas, and damaged condenser ( caused by the useless lower grille in Honda bumpers, with holes big enough for a blackbird to fly through ), the hole in the condensor will obviously cause low gas. I hate shonky garages who just replace big expensive lumps because they lack the skills to diagnose the failure of a £20 item. The likelyhood of failed compressor and relay at the same time is very remote, the failed relay stops the operation of the magnetic clutch that connects compressor to main belt drive operating which obviously stops the compressor performing any compression. Personally would be wanting some money refunded.... I hope they returned you old ( but working ) compressor to you.