You can test ST-10 simply using a 3.5mm to RCA Y cable using analog source (headphone out from smartphone or laptop, remember to turn down the volume).
But you have been using the same system for over a year, and then suddenly you have problem. So now the problem seems to be ST-10 shutting down after playing for some time. I suspect it is the power supply relay board (this tiny board turns on the power shortly after AC switch is on, to avoid turn on pop) failure. The transformer inside ST-10 is unlikely to failure. And this can't be the amp board either (otherwise it would have no sound at all).
Regardless, we can ship the parts to your dealer/distributor for service, it will be faster than sending the ST-10 back to the distributor. Your dealer/distributor would know how to use our helpdesk to request for parts.