Well, no. You can't do that either. You could if "it" referred to the nearest noun, but it doesn't.
"I had downloaded Puppy 4.1.2 and burned it to a DVD. But the DVD cannot be inserted into a tablet because it has no DVD drive." This is better. The last 'it' is meant to refer to the tablet, but we only know that from the understanding that a DVD logically can't have a DVD drive, so it must refer to the tablet.
You can need to consider the grammar and the context. But the simplest thing to do is to write your sentence and see if there's any ambiguity. Sometimes, you're stuck with "I had downloaded Puppy 4.1.2 and burned it to a DVD, but the DVD cannot be inserted into a tablet because the tablet has no DVD drive."
If you have to repeat words to make the meaning clear, then that's what you do.
If you wrote "I downloaded Puppy 4.1.2 and burned it to a DVD, but it doesn't work", it's unclear whether you're saying that Puppy doesn't work or the DVD doesn't work.
I don't think I've contradicted myself, but you can let me know if I have.