Actually, Argentina and Germany operate on different GSM bands. Argentina operates on 850/1900 just like Canada and the US. Germany operates on 900/1800 like most Euro countries. If you have a 900/1800/1900 triband phone from Germany, you are supposed to get service, since Personal only uses the 1900 band. Claro and Movistar use both, 850 and 1900. If you have a 900/1800 dual band phone, you will not have reception at all. You must have a quad band phone, 850/1900 dual band phone or an 850/1800/1900 tri band phone for it to be fully functional in Argentina. Quadband phones work worldwide. Triband phones work worldwide, but might have some limitations.
Even if you get a phone without contract, it might still be locked. If you get a phone without a contract from a service provider, its very likely that its still locked to them. You might need to get it unlocked or like erindanelle said, make sure its not on flight mode. For unlocked phones, its suggested to always puchase an unlocked OEM phone.