Need firware update for LG DVD Rom but cannot find, solution? Cylindrical disc errors

I have a Gateway computer and am recently having poblems with my DVD rom drive. It just doesn’t want to read some discs all the way when backing them up uding Shrink DVD and DVD Decrypter. I have taken it out of the computer and pinpointed it to LG as the maker. The model is GDR-8160B. It is from around 2002 and I was trying to upgrade the firmware as I think that may be the problem. I keep getting cylindrical disc errors so someone suggested to upgrade the firmware. I have been to the LG website but this drive isn’t listed. But they do have model GDR-8161 but unsure if I can use that one. Should I just buy a new DVD drive for $25 and forget about it? Suggestions?