Is it just burned games or is it with legit discs as well? If it's with both there's a very good chance that you've got burnt out capacitors in your console; this is a very common issue with the PC Engine Duo apparently. The first half of this video goes over this exact issue in more detail and shows the repair process; https://www.youtube.com/watch?v=zszqex-b48I

If you wanna try following along with your console you'll need a soldering iron, high tin to lead ratio solder, a solder sucker and a steady hand, along with the replacement capacitors.