Odds are the case is moulded from ABS. To close the holes, plugs made from ABS, either milled out of sheet or 3D printed, with a lip on the interior side, glued in place with solvent (pipe) cement would probably be the best option for strength and long-term stability. Then you need to achieve the best cosmetic result. If the front panel doesn't have a high gloss finish that could be easily over-painted, that may be rather difficult. Worst case, after filling remaining defects, you may have to settle for selectively painting the plugged areas to an acceptable colour match, accepting that they will still be visible and that the colour match will deteriorate as the case colour continues to darken due to aging and ambient UV.