I'm not a professional arborist, but I do have a little experience in landscaping and pruning.
It sounds to me like the lower half of the old trunk is sprouting multiple branches/suckers out of it. There is also a sucker that has come up from the root stock.
Is that correct?
If you are certain that the tree is not grafted, then the sucker coming from the root stock, being the strongest one, should be selected to live. Prune all the others off, including the old trunk if you can do so without harming the sucker that you've selected to let live.
However, if you aren't certain if it is grafted or not, then select the strongest sucker coming off the dead portion of the trunk and prune the rest off.
There may be a way to tell if the sucker coming from the roots is a true form that you want, but it's not a 'sure-fire way to tell'. Compare the leaves/bark/every aspect of it with the others. Do you see any differences? If there is no difference at all then chances are it isn't grafted (but there is still a chance that it is grafted). If it does look different then it is most likely grafted and I would not select the sucker from the root-stock.
I had this same problem with a Red oak in my backyard when I moved into the house. Looked like a 7' tall red oak (likely planted when the house was built in '05) had died. I wasn't even sure if it was alive because last fall/winter when I moved in it all just looked dead. The main trunk etc was still there but rotten. All around it were suckers/shoots coming up, forming a beautiful Red oak shrub. That was perfect if you wanted a shrub, but I wanted a tree. So this past spring when things greened up and I was able to confirm that it was actually alive, I decided to prune it back into a tree. The nicest couple shoots were actually pretty strong looking, but they were all clumped together and it was going to be very difficult to properly prune the others off without harming the selected shoot. Off to the side, however, there was a sole shoot that wasn't bad. It was a little stunted, and a little twisted, but this is a yard tree so straight grain etc wasn't my priority. I selected that one to live, and I pruned off the remainder. Because the roots were well established to support a 7' tree, the little sucker took off like mad. In 1 growing season that shoot went from 3' to 6' tall and it's nice and bushy now. The difference was that I trimmed off all the other shoots, and that allowed the roots to support that one shoot very well.
If you do the same thing with you tree (trim off the suckers) you're going to be quite surprised in how quickly the selected shoot takes off and grows.