Question: Why did it take Starfleet 100 years to find the remains of the Borg and their sphere in the Arctic?
Question: Is the captain's dog still alive?
Answer: Yes. Porthos survives this episode, although many a viewers' sanity and the show's ratings were not so lucky.
Other mistake: Two Borg are discovered North of the Arctic Circle. One is covered in ice, the other encased in ice. Carbon dating shows the wreckage to be over 100 years old (to tie it in with Star Trek: First Contact). The Borg are inactive and unable to repair themselves until they are "defrosted". The temperature above the Arctic Circle doesn't usually drop below -100°F. The Borg have been shown to work very well in the vacuum of space which is 3-4K (roughly -454°F). If they can survive that, even being frozen in a solid block of ice would not slow them down. The nanites have to be in their "blood" and operate at the cellular level. That cannot be damaged by re-entry and the crash.
Dr. Phlox: When was the last time you slept?
Commander Tucker: T'Pol tattling on me?
Dr. Phlox: She's worried about you.
Commander Tucker: I appreciate that, but I'm holding this ship together with spit and bailing wire.
Dr. Phlox: Six hours.
Commander Tucker: Two.
Dr. Phlox: Four.
Commander Tucker: Done. And remind me never to buy a car from you.
Trivia: When Travis is in his old room talking with Nora about Enterprise, look on the bookshelf behind Travis. There's a large white book about Chicago gangs of the 1920's. In the original series episode "A Piece of the Action" it is determined that 100 years ago the ship Horizon accidentally left a book about Chicago gangs which influenced the entire culture to mimic the mobster lifestyle. (00:20:55)
Chosen answer: That's just how long it took. We are still digging up artifacts that are thousands of years old. It takes as long as it takes. Add to that the fact that, at the time the Borg came, Earth was still recovering from a massive war, and it's safe to assume that it took a while for complete exploration and research missions to get going full bore again. Also, they didn't know to look there. There would be no reason to simply head off to some random site in the Arctic and start digging.
Garlonuss ★