Tense consistency
My textbook says that facts or truths which do not change can be present tense, even when the whole sentence is in the past.
Example sentence from my textbook;
Galileo Galilei KNEW that the earth GOES around the sun.

The station master TOLD me that the first train STARTS at five.

In contrast, another example;
DID you say you ARE/WERE Japanese?
My textbook says "were" is commonly used because of the tense consistency although the person's nationality never changes.

Is this true?
Galileo KNEW + WENT and the station master TOLD + STARTED; do these also work?

My sentence;
I noticed that this machine did/does not work.
In this case, "did" or "does"? (*I know that this machine still does not work, so this fact is still lasting)

Thank you,

Question

Tense consistency
My textbook says that facts or truths which do not change can be present tense, even when the whole sentence is in the past.
Example sentence from my textbook;
Galileo Galilei KNEW that the earth GOES around the sun.

The station master TOLD me that the first train STARTS at five.

In contrast, another example;
DID you say you ARE/WERE Japanese?
My textbook says "were" is commonly used because of the tense consistency although the person's nationality never changes.

Is this true?
Galileo KNEW + WENT and the station master TOLD + STARTED;  do these also work?

My sentence;
I noticed that this machine did/does not work.
In this case, "did" or "does"?  (*I know that this machine still does not work, so this fact is still lasting)

Thank you,

Answer

In the USA we would say "DID you say you ARE Japanese?" Were can be used but is not common.

These are both correct as is:
Galileo Galilei KNEW that the earth GOES around the sun.
The station master TOLD me that the first train STARTS at five.

"I noticed that this machine does not work." Is correct.

Answer

For your sentence I would say, "I noticed that your machine does not work." If I were going to use "did" in a sentence similar to this, I would simply say, "The machine did not work." Because you are using the word "noticed", it just makes better grammatical sense to use "does." Hope this helps!