Is it possible to get a trademark for my company for a name having the trademark status "Dead"?

What trademark do you want to register, for what products and/or services and in what countries?
And what are the products and/or services designated by the prior one?

The key in Trademark is whether there is a "likelihood of confusion" between a proposed mark and an existing mark. Since the Trademark is considered "dead" this would mean that it is no longer in use. Thus there would be no "likelihood of confusion" with an existing mark as there is no existing mark. Depending on how far apart the "industry sector" you mention is, even if there was an existing mark, the categories could be so far apart as to not have a "likelihood of confusion" anyway.