Kim,

In order for this non-Catholic to marry a Catholic, the Church would have to determine whether their prior marriages could be annulled. If either were valid [and/or] sacramental, and there was no preexisting reason which could allow the Church to grant an annulment, no Catholic could marry that person without committing adultery and being prohibited the sacraments.

With respect to the ability of the person to become a Catholic, that is an entirely different story.

The person can seek to enter the Church but must remain single unless the previous marriage(s) can be annulled.

Finally, a Catholic cannot marry without a Catholic ceremony and still remain in good standing with the Church.

John