I always carry a hand transmitter when I fly. Licensed ham, amateur extra level in the US + an equivalent Japanese license. Some transmitters can broadcast on aviation frequencies, though I am not sure about the legality of those - probably depends on the country and whether or not you have a license there.
Couldn't an ACARS or other data message be sent to HQ then telephoned to ATC by someone on the ground? The 777 has something like 3 VHF radios and probably 3 VHF antennas as well, but there are also the HF antennas and radios which should be able to contact somebody, somewhere.
My confidence in Asian pilots is very low. I've been running a training program for the last 5 years trying to teach Asian pilots how to deal with this kind of problem (Fixation, poor crew coordination etc). I wish I could get them all to come to my course to avoid stuff like this incident.
It seems very unlikely that all radios and antennas could fail in midflight.