Sounds (sorry for the pun) as though you've tried everything. Next step is how confident are you in opening the unit. It may be a wire off the back of the jack plug, or a bad soldered joint if it mounts directly to a circuit board, or a faulty socket itself which may need replacing, in which case is a spare available or is it an Archos part; or returning to Archos for repair
Is it under guarantee ??, see my post about 2 year EU guarantees.
Personally, if not guaranteed, I would open the unit.
Re the other poster, Mr Bangitandsee, I'm of that school too, but its not that useful with todays technology.
Best of luck.
There is another poster who describes how to open the 705, probably stuff on Youtube too.
Just another thought, the sound does go from the speakers when you insert the headphones doesn't it, cause there is a setting that outputs the sound only to the speakers
Settings..Sound..Built in Speaker.. make sure this is set to Automatic then sound will switch from speakers to headphones when they are plugged in..
Apologies if you already know all about this.