I cleared the back-up with a plunger; there was no backflow that had caused the problem.I waited a while. Then proceeded with plunging 3 times(25-50 plungers each)... all with the same results. How can this problem be solved?
Thank you

If a few buckets of water poured down the toilet bowl, won't clear the blockage, after plunging, then you will need an auger. Unclear if you mean the toilet won't flush sufficiently, then remove the lid and see what happening.