The phone doesn't have support for the 1700 band, but will work on the 2100 band offered by your provider. The biggest problem you face is what is the difference between bands for VTS, typically network providers will offer a faster network and or more coverage on one of their bands. If in Chile this is the 2100 band you are away laughing.
Just had a look at the specs of your HTC Desire HD and the news is bad.The new HTC one will the same as your previous phone on that network.
I don't understand what you are saying about your phone not on 3G, the 2100Mhz network is 3G, however it would seem that your provider is offering it's premium higher speed services on 1700Mhz.
I suggest you go to
www.gsmarena.com then search for brands of phones that have 1700Mhz radios. So got to say HTC, and under bands select 1700 then filter, you will find only 13.
After checking this, scrub the above and only use it as a super rough guide. Because it states the Sony XZ as 1700Mhz, but no Sony website claims this that I can see.