The TSA Restriction
The restriction you mentioned does not apply to all flights towards all destinations. It is a new rule which is slowly being implemented across continents. If I am not mistaken the US were the first, followed by UK. I could not find any official reference covering the status by country. All I stumbled upon were local online newspaper articles for US and UK.
EDIT: I found a bit more information on this regulation. It might be helpful. BBC says that the TSA delegated both airports and airlines to carry out the necessary security checks:
But airlines and airports are obliged to meet security standards set by the Transportation Security Administration (TSA) in order to carry on operating non-stop flights.
Moreover, it seems the regulation will be enforced by the UK, France and Germany:
The UK, France and Germany have all said they would comply with the American demands.
Finally the it is unclear where the checks will be carried out. I think it is safe to assume that checks could be carried out both at the security checks held before entering the international area of the airport, as well as just before boarding. The latter making more sense IMHO because anything can happen between security screening and boarding.
Checks will be carried out at London's Heathrow both at passport control and boarding gates, while a spokeswoman for Manchester Airport told the BBC that device power checks would only be done by airline staff at departure gates.
So basically the rule becomes bring a charged device.
Either Check-it In of Leave-it Home
In your case you will probably have to check-in the device when flying out of Argentina into the US and you should have no problem on the way back to Argentina. (This is also because supposedly the device will be in full working order then, and charged.)
Checking-In Luggage Safety
You could try covering it up with (dirty) clothes and burying it deep inside your luggage so as to make it the last available item for potential thieves. If you are worried about it being x-rayed and then stolen you could try wrapping it up in aluminium foil, or you could put it in a lead bag, like those used for protecting photorgraphic film. However I do not know what happens in that case -- since the content of the bag is not visible from the x-ray your bag might just win a manual search. And if the security officer is handsy and really needs your device, well...
Ok for completeness sake you can also film wrap your check-in luggage with those services you find in airports. I would imagine that items packaged this way tend to be less of a target for thefts. Moreover you would be insured, but do check the details of the contract for that.
You could also consider buying a pelican case or similar for added protection.
Finally you can add padlocks and other locking devices to your suitcase to make it safer.
All of this does not consider the problems you might incur in with local customs, but I'll leave that for another question. :)