He never gave up. And now, at 29, an age when many baseball players are near the end of their careers, Kubiuk's is just getting going.
After spending a few seasons in Mexican and independent leagues, Kubiuk got an offer last month from the Arizona Diamondbacks organization.
"My heart dropped a bit. I don't think I responded for a few seconds. In the end, just super exciting to get that phone call," Kubiuk said.
It is the opportunity Kubiuk and his family have been praying for, but had almost given up on. It is big news in the Barrington community.
"It was the answer to prayer. Daniel has been doing this since kindergarten, playing with second graders," father Carl Kubiuk said.
"We were so excited that God would give him an opportunity to take that next step," mother Susan Kubiuk said.
He's been a talented athlete since he was a little boy, playing with the older kids in little league.
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In high school, Kubiuk was drawing attention from college programs all over the country, until his injury.
But, he could still play football. So, he walked on to the program at Northwestern, and became the starting punter.
"He's always been a talented athlete. What takes it to a different level is the continued dedication; his story is one for all of us to hear. It's bigger than sports," said Pat Wire, Barrington High School baseball and football coach.
Kubiuk was eventually able to return to baseball for a season at Northwestern as a walk-on to the baseball team.
But he then put baseball aside until after college, when he played with a few small independent and Mexican league teams.
He was at the point where he was pondering his future when he got the offer to join the Diamondbacks organization.
Now he's aiming to make it a couple jumps from Class Double-A, where he is right now, to the big league club in Arizona.
"There's just something about baseball that I'm tied to. I love it. It was my favorite sport growing up," Kubiuk said.
Kubiuk still lives in Barrington in the off-season. And his former coaches say he is a great role model for younger athletes, helping them learn to never give up.