here are some ideas to consider:
1. In the city field, try inputting the city, state, zip, country and in the address field, do NOT putting in the city, state, zip, country.
2. Go to tripadvisor.com peru forum or lonelyplant thorn tree Peru branch and post your questions there. Plenty of people booked Star there. Someone there must know.
3. Call your CC and find out if your charge went through (from your e-mail) and also check your e-mail spam blocker to see if their return e-mail might have gone into spam.
4. If all of the above fails, as a last resort, find a travel agent in Peru and see if they can book it for you and make sure they don't book you LAN.
Most of the time, the problem is you have to verify Visa if you are using a Visa card. When I booked Peruvian Airlines, my ticket went through fine and they actually called me to verify the charge. Are you trying to fly from Arequipa to Cuzco or Juliaca, which Peruvian Air does not fly? :-)
Good Luck and travel safe!