If you can boot to the recovery mode then you have access to Disk Utility.
Not accepting yur password for the User probably means either it is trying to access a different drive/user or the User got corrupted (an old problem not seen much anymore).
When Recovery mode comes up, if I remember correctly, you see a screen with a language choice then you proceed to the next screen which could be an installer or choice screen.
At the top of the window you will have a menu bar, in the rightmost menu you have access to some tools, like Disk Utility, Terminal and such.
Run Disk Utility, see what drives list on the left side. Choose your start up drive and then run Disk First Aid on it.
Also, if things fail to resolve but you are in the Recovery mode then you will have access to use the Time Machine backup drive.
I d hope it is a separate drive.
Again, when I resolved my wife's iMac problem I was able to boot holding the Option key down and saw the drives list on the scfreen.