It sounds like you're dead on the right track. As I was reading I'm thinking man you need to try the unit on your known good PC.

Sylvan, That Tascam 2x2 can be powered by either USB or an external power supply. If he is using USB for power maybe it is not giving enough power to the unit to run properly.  The  same thing can happen if he is using a powered or non-powered USB hub.
 
You didn't mentioned how he is powering that unit so I thought I would bring this up.

With my Tascam us1641 you need to plug it is "DURING" the driver installation, not after. 
 
Not sure if this will be the same for the 2x2 but I found you had to pay attention more so than say when I install my Scarlett drivers. 
And very annoying is you also have to ignore windows asking if you want to install the driver.
 
The proof is once installed get him to go to windows audio devices and you should see the tascam, if not try again.  

I was having troubles with Vegas (no prob w/ SONAR) with my UH7000/US 20x20.  Part of it may have to do w/ the 20x20 having set itself as the default driver. Switching to the 7000 w/ Vegas crashes Vegas.  I reset default to the 7000 but didn't have any more time to play w/ it last night.
 
Perhaps part of the problem is w/ the default audio.