Carbon-based molecules that once floated in interstellar space are thought to have been later incorporated into Earth, providing the raw materials for life

"We are stardust"

To limit the search to carbon-based molecules is probably a mistake. Life in other parts of the universe may have evolved entirely differently, although I would think it would be based on an atom with similar structure and properties, like silicon, although it may not necessarily be the case.

There are generally 7 traits which most biologists look for to tell if it is 'life' or not, but those are based on life as we know it. It's possible that other life forms are so different than us that they follow only a few of these, or none at all.

"all we are is dust in the air"