This sounds like a hardware issue to me; a brand new Surface shouldn't be doing this. I found a few people who've said that the solution was to get an exchange after talking to Microsoft Support, with one saying that they didn't even bother going through the diagnostics, just sending him back to Best Buy to exchange it.
There is a Surface Diagnostic Toolkit that you can get here: https://support.microsoft.com/en-us...ace-problems-using-surface-diagnostic-toolkit
There is a Surface Diagnostic Toolkit that you can get here: https://support.microsoft.com/en-us...ace-problems-using-surface-diagnostic-toolkit