I believe that you are talking about in-vitro fertilizer (ivf). I think it is quite expensive, my guess is a few of $10,000. There is another one I heard of is artificial insemination (iui) in which they give her fertility drug to help produce more eggs and directly inject sperms into her.
I have a relative who had ivf done oversea. They now have 3 little children from this procedure.
Well, before you go that far, I would try the natural way first. Again, if my memory is right 1 in 3 of women who have her tube untide are able to get pregnant again. Consult your doctor about your plan. Good luck.