Can you fresh start a computer that has no keyboard or mouse for input?
No, you're right. You can't. I didn't realize that you can't use any of the USB ports at any point. And if they won't even work at startup, that's REALLY odd. Not working once the OS tries to load is one thing, but them not working at any point is another.
If they worked at startup you could maybe try a Windows 10 startup disk.
About your only option now is either seeing if Dell will send you the OS disk, or if your product key is embedded in the BIOS, download your version of Windows 10, either using someone else's machine, or have someone do it for you, write the ISO to disk
out and format it using someone else's machine, then put it back in and reinstall Windows 10.
Regarding the Windows 10 ISO, though, you have to get it using the Media Creation Tool. You can't download it any other way, as you've seen.
But, again, even with a user created installation disk, you're not going to be able to install it if you can't use the USB ports.
For a Windows 10 update to screw something up THAT bad is very odd. Try disconnecting the HDD or SSD that has the OS on it and then try to start the computer with the keyboard attached. If it works when doing that at least you know it didn't somehow mess
up your BIOS. Then try reattaching the OS SDD or HDD and see if you can start it with a Windows 10 Startup disk and your keyboard. If you can get that to work, you can get into your recovery partition and recover the desktop.
Why your USB ports won't work, even at startup, is strange. I've never heard of that happening before.