Another update: Today; I had my hands on a DVD Movie, and it plays it.
So, I don't know. Either my CD-Rs and DVD-RWs (all of them) got affected with the heat, humidity, etc. [They are all kept in a nice shell.] (to check that I will need to get new CDs/DVDs to write and test).
Well, it is a good thing that it reads DVDs.
If I get my hands on new CD-Rs and DVD-Rs, I can check if it will read what it writes to those new ones.