So, Eleven Rack is your interface, but you had to use another interface's (your old sound card) mixer to mute the incoming signal; can't you do the same thing with the computer you have now?
Or were you using the audio outs from the Eleven Rack into the old sound card and not the USB connection?
According to Avid's web site, the Eleven Rack records both the dry signal and the processed signal simultaneously. Is that what you're trying to stop? Or at least trying to stop hearing the dry signal?
Won't clicking the Mute button on the track recording the dry signal work?
Maybe not, I've never checked to see if that will mute a recording while recording.