It is a TI chip on the card. I'll have to pull it to see what brand the card is, though. Bapu may know.
It is PCIe.
My DAW computer uses VIA without problems (as someone in a very old thread wrote, "you got lucky").
 
I'll go through these recommendations on my days off and see what happens. I just think it's strange that the FW card was seen by Windows when I first installed it, but never again.
 
Thanks everyone for chiming in. I'll let you know the outcome.

So, nothing worked, as far as I can tell. Still no device showing in Device Manager.
I ordered the FW card firebird recommended above (great service from Amazon, by the way). The installation instructions say, "Locate an available PCI-Express slot (preferably a PCI-Express 2.0 slot)".
How do I determine if I have a 2.0 slot and which one of the two expansion slots I have is it, or are both of them 2.0 slots?
All info appreciated.
 

Since Windows is not "seeing" it, the next step is the BIOS.  Some BIOS will identify added cards and some will not.  However as Windows is not seeing it likely the BIOS is not either.  Next step is to reset the BIOS (Clear CMOS memory).  Some motherboards have a jumper to clear CMOS, but the best way is, with the PC powered off remove the CR2032 CMOS backup battery on the motherboard for AT LEAST 10 minutes.  Replace the battery, observing polarity and then power up and Check the Device Manager to see if its installed (or has an error code).  If there were any BIOS customizations those will have to be set again, because of the clearing. 
 

Thanks, firebird, but that's the old FW card I installed last year not being seen. I bought a new one and am trying to determine if I have a PCI-Express 2.0 slot in which to install it, to replace the old one. Hopefully, it will be seen, and work, on this Win 10 machine.

I would think it will work OK.  
 

The best way to know what the slots are on the MB is to google your MB and download the pdf for it.

Have you tried the board yet?
 

fireberd
Have you tried the board yet?
 

Yes. Recognized and working, but it just won't communicate with the Saffire.
I guess I have to accept that it won't work on Win 10.

It should work.  My Saffire Pro 40 went "bottom up" (died) back in the Win 8 days.   I liked it and thought it was great until I got something else to replace it and much better recorded audio.  
 
Before it died I had some problems with the Firewire interface, it stopped connecting so I was using my backup MAudio Fastrack Ultra backup unit.  I kept messing with the Saffire Pro 40 but neither Firewire port would work (connect).  Then all of a sudden one of the Firewire ports worked but the other didn't and I started using it again until it died completely.
 
The MOTU 896Mk3 Hybrid I have now is connected via Firewire and I'm on Win 10 (current fall creator's upgrade).

Saw this on the Q&A section of the link Firebird posted earlier.
 

The SD-PEX30009 model is incompatible. It uses the TI XIO2213A chipset will not work with any Saffire devices. The SD-PEX30016 uses the TI XIO2213B chipset and has been recommended by Focusrite for use with their legacy devices https://support.focusrite...-gb/articles/207546925

 
I have the PEX30009, which works wonderfully with my legacy M-Audio FireWire interface, has worked on both Win 7 and Win 10.
 
But based on this comment, it appears that the Saffire only likes the TI chipset included on the PEX30016 model.