USB KB & mouse disabled by Logitech software & dead on reboot

An old Logitech 250c webcam was giving distorted audio, so I downloaded and installed the latest aoftware. After install, the system needed a reboot. But on bootup the usb wired keyboard and mouse were dead. The boot halts at the "Choose your keyboard layout" screen. Without a mouse or keyboard I can't do a thing. Win 10's automatic system repair didn't fix it. I changed usb ports, no joy. I've created a Win10 recovery disk from another system, and while it boots and the KB & mouse work, all of the repair options fail. I can get a command prompt and that's it.
The KBM power up and are shown connected in the BIOS, but when the Win10 startup screen appears the usb power is cut to the KBM - NUM lock light & the mouse LED go dark. The computer (a Win7 HP) doesn't have PS-2 ports. Only usb. I've removed an aftermatket usb3.0 card. Nothing helps.
It seems to me that the Logitech setup has written itself into a wrong place in the boot order somewhere. But where and how do I get around this?

Thanks to all for your replies. To clarify..
1. To enter Safe Mode, you have to be able to boot into Win 10 or already be in Win10. I'm locked out by not having KBM. At least everywhere I've looked tells me so. If there's a hidden back door in, please enlighten me.
(BTW, Microsoft, Safe Mode is useless for troubleshooting if you can't cold boot into it!!!)

2. There is no "Legacy USB" in the BIOS. Both the Keyboard & mouse appear in the USB section of the BIOS. I've moved them to different ports and they always show up in the BIOS as connected to their ports, whichever ones I've moved them to.
The BIOS is a Megatrends v6.11 for an HP AMD desktop. Not sophisticated but neither totally stripped down.

3. Logitech setpoint - I'm unsure as to what version I tried to install. I searched for the latest driver package for the 250c webcam on Logitech's site & downloaded it. The install appeared to go normally, the final screen being the need to restart. Once restarted, after the BIOS loaded I got the Win10 initial boot screen with the blue flag, a flash of a partial black screen, then the Win10 "Choose your keyboard layout" screen. But the KBM were dead, no power from the USB ports, as the ports go dark just after Win10 starts to load. From this I infer that the Logitech setup has written itself into the top of the boot order to disable the KBM drivers, but the command to load Logitech drivers comes too far afterwards.

4. I can get a command prompt by booting to a Win10 recovery disk I made on another machine. When I do this, the KBM stay powered through the boot, and I can select a US keyboard from the layout screen. I can then look at the hard drive in question, navigate through hdd's and directories, even read some of the logs using "type" command - well read some of the logs until the buffer overflows.

All suggestions welcome!

Thanks for the response.
Let me clarify further...
1. I'm not sure if it was setpoint or just a driver package I downloaded. I can't get into the system to look at the downloads.
2. The only devices connected to the USB bus are the keyboard and mouse. Both of which lose power the instant Win10 gets to the automatic system repair.

Got a PS2 port on the PC and a PS2 Mouse or Keyboard? or a PS2 to USB adaptor, sometimes, well a few years back, you got one with a USB keyboard for plugging into a PS2 port?