Is your Keyboard ps2 or usb? The onscreen keyboard is the accessibility one correct at the login screen? What happens if you reboot it and keep hitting F12(or whatever key shows up in the top right for boot menu) do you get a boot device screen?
Oh good catch then it might be their board is damaged and keys are stuck, that would explain why they can't input with the onscreen keyboard as well. I read it as Pavillion not Inspiron, wrong company
will ask one more question for the OP can you get into bios? pressing F2 when you start laptop? does the keyboard work their like the arrow keys esc key enter key?