win 10 always asks for a password to login, unless you have it set up to auto logon.
Do you know your password? Confirm your password works by going
here - can also use that site to change password if its not the correct one but you own PC. IT will send the password change details via email to address linked to PC.
I can't help you get into PC without password, but I can help you try to fix a PC that refuses to login.
The lack of network access could be reason password isn't working, as I think PC checks for network password changes before logging in. I have had some weirdness with the box just not showing up at all.
On the screen before password screen, where it normally shows Ease of Access, Network & Power in bottom right corner, click the power button
While holding shift, press restart button
this should load you into windows recovery environment (a blue screen).
Try running start up repair
choose troubleshoot
choose advanced
choose start up repair - this will scan PC and maybe fix this - will ask for logon info so you need the password to go ahead.
try safe mode:
choose troubleshoot
choose advanced
choose start up options
hit the restart button
choose a safe mode (it doesn't matter which) by using number associated with it.
PC will restart and load safe mode (need login info to get in)
Sometimes just going into safe mode and restarting can fix oddities like this.
I think most of the options here need a password, you can try system restore as it might just be a system setting causing the bug.