Latitude 5420 Can Get into BIOS but Cant Change Boot Options.

What about one time boot menu (F12) does it do the same thing ? 
Model has a modern Tree bios which lets you use both keyboard and Mouse as well touchpad. Have you tried a mouse. Have you tried an external Keyboard.

Perform a hard reset : Force power button for 30 seconds. 

if the keyboard and mouse are not operable in both F2 and F12 menu. than you need to perform a BIOS Recovery as system firmware may have been corrupted.  

Wow,

that is really some weird behaviour. The first thing which came into my mind is a very harsh one, but might be worth out trying:

https://www.dell.com/support/kbdoc/en-us/000124377/how-to-perform-a-bios-or-cmos-reset-and-clear-the-nvram-on-dell-systems?lwp=rt

Hope this might help.

Cheers

Fullyard

Gave all these a shot and no luck.

F12 boot menu was actually different, only the singular option to boot from hard drive. Tried the touchpad, external mouse, and external keyboard. When I try to tab or arrow to option it just skips over as if I don't have permissions to do so.

Weirdly enough I tried to do  BIOS Recovery after all this and it went on for 12 mins holding down Ctrl + Esc to no avail, the BIOS recovery never popped up. Let it go and display did the cycle color diagnostic but then booted to hard drive again.

Checked BIOS Event Log after all this and found "Alert! BIOS recovery file not found."

Going to attempt this now (08/21/22) as I figured I'd give the recovery a shot.

Uff, that's a hard nut. Were you able to clear the bios battery, if it's possible with your model?

Another thing which came into my mind.

There is something like a dell recovery usb bootable stick you can create, with windows as well as the os recovery stuff on it.

Maybe you're able to boot from that one and flash stuff back and get into a factory reset kind of state?

https://www.dell.com/support/kbdoc/de-at/000125230/how-to-create-and-use-the-dell-recovery-restore-usb-drive?lang=en

Wish you the best and hope you can restore your momentarily haunted Notebook there...

Well I unplugged 4 cell battery and drained the residual. Tried to boot up again and was able to get into BIOS but now no trackpad or mouse function (joy). But same issue persists, it skipped over the option to change boot order and arrows to change were unselectable as well.

Going to give this dell recovery usb bootable stick a shot now.

Unfortunately no luck here as well. Now neither the BIOS boot list nor the F12 One Time Boot Menu are showing the USB (dell recovery USB bootable stick). Not sure if there are any other factory reset options.