Make a reliable backup if at all possible, for instance with a Time Machine disk connected it should run automatically, or tell it to run from the Time Machine icon in the menu bar. Or if you have one already that at least has backed up your files, then you are somewhat protected. If you can get Disk utility to open, the Restore button may also allow you to make a backup.
Was your Time Machine drive the one that wasn't ejected properly? If so, your backup might not be reliable.
Is your mouse connected and working properly? If it isn't, it might look like finder isn't responding.
Boot into Safe Mode, holding Shift key, be patient as it can take quite a few minutes, it is checking many things. Can you do things in the Finder in Safe Mode? Then restart normally and test again.
If still no Finder, boot into Recovery and run Disk Utility First Aid to check/repair the disk. Rerun it until it finds nothing to fix. Then reboot normally and retest.
If still no Finder, boot into Recovery and choose the option to reinstall the MAcOS. This is the option that does NOT INCLUDE erasing or formatting the disk, it simply reinstalls the MacOS, it should not modify or touch your user files.
Then boot normally and retest.
If still no Finder, the next step would be to erase/format the disk and install a fresh system but don't proceed with that yet, you need to find a way to reliably back up your files before doing that. If you have been unable to execute a good backup, one option would be to enable Sharing in the System Preferences and to copy your most important files (I would copy everything in your user directory) to another Mac through the network. Another option is to boot into Target mode and connect to another Mac and copy your files that way. Hopefully one of the earlier steps resolved the issue.