In reply to zimpara:
Fly to Buenos Aries then get the bus to Mendoza.
Cheapest route I found when I went to Argentina was Heathrow to São Paulo, São Paulo to Buenos Aries. I flew out on Christmas Day, which made it cheaper.
You can also fly to Buenos Aires via Madrid or Miami. The bus services in Argentina are great, well set up for mammoth overland journeys. I went from Buenos Aries to El Chalten, the first leg down the Atlantic coast to Rio Gallogos was 40 hours.
I have no experience of doing the journey from the Chilean side.
Post edited at 09:26