there are 2 laser (with different power) for writing and reading in a DVD (and CD, BTW) writer.
The less powerful (the reading one) might have a problem.
So, instead of an Windows approach, i would suggest you to have someone lend you a DVD writer, and see if it reads. Likewise, you could test the possibly defective writer in another system.
If it doesn’t read also, the less powerful beam might beam defective, or have some dirt on it.
There are links to clean a CD/DVD reader/writer on the Net, it’s not very difficult when being careful, And you can clean the lens with a Q-tipp.
If the reading problem remains, and you had tried another writer on your system and it’s ok, then buying a new one might be what you should do.