Sierra update - wont recognise external soundcard
Looking at the Q&amp;A for the sound card you mentioned (check the "Questions" tab on the linked website in the comment to the original question) you'll see the first question is about the availability of Mac drivers and the manufacturer response states that none are available.

Looks like your best option is to find a different USB sound solution or get your logic board repaired.

Edit: aha I forgot about SIP. Sierra broke a bunch of driverless stuff with SIP. There are ramifications for disabling it, but if you want to try it check out this Reddit post.