Thanks, everyone who replied. Here's what we know as of today:

The network / hardware guys discovered that there is a BIOS patch for the Skylake i3-6100 chipset. We're still testing, but so far the patch has fixed the problem on the two machines to which the patch has been applied.

We're still seeing the problem on the Skylake i5-6500 and waiting to see if there will be a patch for it as well. I'll post back with details on the patch(es) once we know for sure that's the solution.

-Rick

>Hi Rick,
>
>>Is anyone successfully running a FoxPro for DOS app on a machine with the new i3-6100 Skylake CPU?
>>
>>Our old FoxPro 2.6 for DOS app has run happily on 32-bit Windows 7 workstation machines for a long time, but fails to run on the newest replacement workstations that have i3-6100 Skylake processor. Symptoms are that the ntvdm.exe process starts up as expected but then hangs with nothing visible happening in the command window it's running from. The task manager shows ntvdm.exe running at 25% CPU - 100% CPU on the one core that ntvdm.exe is using and nominal CPU % on the other three cores. Memory usage does not fluctuate.
>>
>>We realize this problem could be due to something else but at the moment we're focusing on the hardware because the network guys can't identify any other differences between these new workstations and the slightly older ones on which the app runs as expected in the same environment.
>
>There has been recent talk about limited support for SkyLake on Windows 7. That may just be Microsoft trying to push folks to Windows 10, but it made we wonder if SkyLake support was harder than previous chips. Maybe there are some new/beta drivers out there that would solve your problem. Here's an article:
>
>http://www.zdnet.com/article/heres-microsofts-list-of-skylake-devices-that-will-be-supported-when-running-windows-7/#ftag=RSSbaffb68