Yep, tried that last night. Still nothing. Thanks for your reply!!

Try this, first:

Disconnect power cord from rear of PC and press/hold power button for ~30 sec. The motherboard LED will go off. Now reconnect cord to rear of PC and see if it boots now.

Thanks again, RoHe. I tried a different cable and went directly to a wall outlet last night to no avail. When I get home from work, I'll try thto BIOS battery. I already checked the connections, blew out the dust, and checked the button on the back of the case. Nothing...

If you're using a power strip, surge protector or UPS, disconnect those and connect PC directly to the wall outlet.

Try clearing BIOS next: Power off, unplug and press/hold power button for ~15 sec. Open case and remove motherboard battery. Press/hold power button for ~30 sec. While you're in there, check to make sure all cable connections are secure on the motherboard and drives and use some canned air to clean out the dust. Reinstall the battery (might be good time for a fresh one), close up and see if it boots now.

If that doesn't help, it may be a failed power supply...

Well, none of that worked so I'm gonna guess that it's the PSU or the motherboard. Bummer.

Additional question: can I get a replacement PSU locally, or does Dell use a proprietary PSU?

Not a proprietary PSU in the XPS 8700, but if the warranty hasn't expired, contact Dell Tech Support about replacing the PSU.

Some PSU suggestions for the XPS 8700 in the post by Dan-H on 4-4-17 in this thread:

en.community.dell.com/.../20009061

There are others that should fit too.

Forgot to mention that this computer was purchased exactly two years and four months ago. I'm pretty sure that the warranty is long done by now.

RoHe, thanks again. I went and bought a PSU, and... Nothing. At this point, I'm guessing motherboard. Bummer. I guess I know what I'm doing this weekend!!

Bummer about the PSU...

You have a 1-year warranty from Dell, unless you purchased the optional 3-year warranty. Go to the Support page and put in your Service Tag. (Don't post it here.) You should find a link for Warranty status to check it, and hopefully...

Did you replace the motherboard battery?

Have you checked the cable connections from front panel to motherboard?

Power off and unplug, press/hold power button for ~15 sec. Visually check all USB ports to see if one is bent or broken. Use something NON-metallic to separate the connectors if any of them is broken, but that port may never work again.

Try stripping PC down to bare essentials by disconnecting all drives, except boot drive, removing all  PCI-e cards, including video, removing all RAM modules except the one in slot 1 (slot 1 may not be the one closest to CPU).  Clear BIOS by removing the motherboard battery and holding power button for ~30 sec. Reinstall the battery and close up. Connect monitor to an onboard video port and then connect mouse and keyboard. See if it boots now...

Broken power button?  

Read the manual for instructions to remove/replace the power button module.

downloads.dell.com/.../xps-8700_owner's manual_en-us.pdf