Try some USB keyboard. I was going to mention reseting just the keyboard mapping but a factory reset would do that so the next test is with the USB keyboard.
If a new keyboard did not clear this up and the USB keyboard works it sounds like a motherboard issue. Inspirons can be so cheap that the owner will not replace this board.
The letter "L" will not work on my Dell Inspiron laptop but if I type the l and then o it will appear as ol onscreen. If I type LO using upper case it will appear as shown. Now the period key is not working. I did install a new keyboard and the problem persist. I also tried resetting computer to factory setting. No improvement. Any ideas would be appreciated.