I had licenses suspened in 1999 due to 3 DUI'S prior in Michigan Are they still on my record?.

A DUI conviction stays on your record permanently. In North Carolina however, by virtue of something known as the "look back period", any prior DUI committed more than 7 years ago, is not considered when imposing a sentence for a subsequent DUI; the latter offense will be treated as your first offense since the court will only "look back" 7 years into your record.

As for whether or not you will be entitled to obtain a North Carolina license the answer is probably.  You really need, however, to consult directly with an attorney in the area where you move to to find out for sure.