So I believe the DUI law and entering Canada is that you're not allowed to cross the border if it's been 5 years or less since the incident. At least that's what I've heard several times crossing the border with buddies who have DUIs on their records. Since you've been 14 years sober, I think you'd be OK. You could always call a Canadian consulate and ask to make sure you would be alright. If you're really worried about it, you could even ask for a letter in writing from them stating that it's OK for you to enter, then show it at customs if you have problems.
Another option would be to get a special visa. On a trip to Squamish, BC this summer, one of my friends had to get a special visa at the border due to some prior arrest (I believe it was DUI). Not really sure how it worked, but it was good for the week we were up there. He just had to check in with the Canadians at the border on our way back into the states.
Final option if you're looking to ride all the way there; there's a auto ferry out of Bellingham, WA that will go to Alaska. Ride to b-ham, hop the boat, ride into Alaska. Then there's always renting...