My Xbox 360's DVD drive has broken, so few days ago I ordered a new one.

When it arrived I started checking if it can read game DVDs properly. As it turned out, it cannot. I assumed drive which I ordered is broken too. 

I was going to refund when  today in the last moment I found this thread: 
https://gaming.stackexchange.com/questions/39433/how-do-i-replace-an-xbox-360-dvd-drive-if-the-original-drive-is-broken

where someone answered that each Xbox motherboard and each DVD drive have specific DVD key, and they have to match. I had no clue about that.

He also mentioned that DVD keys can be repetitive, so if I get the same key from newly bought drive, it will work.

At this moment I have no idea if my games cannot be read because of mismatching DVD key or just DVD drive damage. How can I tell if DVD keys are matching?