My thought (having always bought my phones at Sprint) is that Sprint stores have service support personal at some of their stores that also can do basic repair services. Even if the phone was bought at Best Buy, the service provider is still Sprint and they should be able to run "tests" on the phone.
HTC One should also have a one year warrantee, and since the phone only has been 6 months old, should be covered unless abused.
So shouldn't hurt to take it to the Sprint store. Sprint is all about customer service. Worth the chance to get it fixed or replaced verses having to pay for insurance, etc. But you don't know until you try and worse they can do is tell you no...