I have a 15 year old DUI which I never took care of. Can I get a drive's license now?

Doubtful. They do keep records you know. It will probably show up.

And they have computers... and they are linked to other computers in other Provinces sharing data.

Not taking care of your part doesn't start any statute of limitation clocks....THEY would have had to take some action towards you in that time, which I think they did....Hiding doesn't let you run the clock out.

I have a 15 year old DUI which I never took care of. Can I get a drive's license now?

NO. It shows up on the DMV computer in every province. Any time you go, to renew plates, licence, they wont give you either.

The statue of limitation is from the time the crime is committed to the time you are arrested or charged.

If you were charged, the SOL stopped at that point. If you were never changed, then it would have ran out

If you were charged, and did not appear in court, most likely there are other issues also.