If the rose bloomed repeatedly in a previous season, it must have been a grafted rose that died back (probably from cold) to below the graft, leaving only the rootstock alive. The rootstock then made shoots and leaves. These did not bloom because roses of this type only bloom in June on canes that survived the previous winter. If any canes survived the past winter, it will bloom next month, but not like your original rose. The original rose is lost forever,

If you replace the rose, be sure to plant the new one with the graft well below the soil surface. This might get it through the winter.

Yes, it sounds like you're left with just the root stock coming up. If you let it bloom and it's red it's Dr. Huey. If it's white it's Multiflora most likely. Or you can just dig it up and get something you like!