The background check is looking for felonies and misdemeanors. As long as you never served time in jail you should be okay. Also, my cousin was convicted in 1990 of a DUI. When she went and took her NCLEX, the State sent her a letter telling her that her license would not be issued until she submitted a letter that detailed how she has turned her life around since then along with reference letters from her employer, ect. She did all of this and was granted her license last week.
With that being said, do not rule yourself out of nursing. Let the school know of your situation and also you might want to call the State Board to find out if this would hinder you from get your LVN.
Best of luck to you