IANAL, but my understanding of trademark law suggests that if the mark hasn’t been used for that long, it is probably technically abandoned. If it had been held by a defunct company, or one that still existed but was no longer publishing a newspaper, you’d probably have no problem.
But the fact that the company that nominally holds it is the one you are proposing to compete with makes me think you will have a problem. Unless they are an extraordinarily open-minded and benevolent bunch, I suspect they won’t take kindly to your trying to appropriate “their” name. And even if you have the law on your side, they can file a nuisance suit that will be a real pain in your neck, assuming their pockets are deeper than yours.
Here’s how I know about this: the first name I chose for my newsletter had a syllable in common with the name of a leader in the industry I cover. (Just to be clear, they aren’t competing publishers.) It wasn’t a problem for two years, but then, for reasons I won’t bore you with, they decided they wanted me to change the name.
My lawyer told me that they had no case, but that it would cost me about $400,000 to defend the name in court, and there’d be no guarantee that if I won I’d be able to recover that amount. So I agreed to settle, meaning they gave me a large sum of money to change the name. The fact that they paid me shows who was in the right: if I’d really been infringing their trademark, as they claimed, they would have insisted on my paying them, or at least giving up the name without compensation.
So unless you have reason to think your competitor won’t make a stink, or have no fear of entering into a legal battle with them, it might be easier just to look for another name.
If you’re really set on using that one, you might consider approaching your competitor asking them to sell you the old mark for a small sum. Your pitch: their legal claim on it is weak and they’re not getting any benefit out of it now, so why not take some cash? Then it’s only a matter of how much you’re willing to pay. Almost any sum they’re likely to name will be less than the cost of a lawsuit.
Of course, they may decide to be assholes about it either way, so be thinking about that alternative name.