Hi Rick,
You said you've been dialing +56 ... I suppose you are using a cell phone to place these calls. One other option you have is to dial 011 instead of the + sign (011 56 ...).
The first number doesn't look right. Unless it is some sort of special number, area code for Pucon is 45 (this is for landlines only, cell phones don't use area codes). So a regular landline in Pucon should have this format: (0) 45 ??? ???
The second number is a Chilean cell phone. There was a change in the numbering system of Chile in 2007 resulting in all cell numbers becoming 9 digit. Digit 9 must be added in front of the cell number(011 56 9 9870...).
Try these changes and let me know if it works. You can also try using a different line to dial out.
Dan