The round objects in the soil sound like they may simply have been fertilizer balls, which are frequently added to potting soil and are designed to break down over time and release additional fertilizer into the soil as the tree needs it.
The tree could have died from many things, but if I had to guess, I would suspect that it died from stress and shock. Unfortunately, many large garden centers will sacrifice the health of a plant for a sale. In your case, they sold you a peach tree with fruit already on it, because people are more likely to buy a fruit tree if it has fruit on it. But, a young peach tree should be focusing on root and leaf growth. Trying to maintain fruit at a young age stresses the plant. In fact, under normal circumstances, young fruit trees do not fruit at all. Greenhouses use special techniques to coax them into fruiting too early and, therefore, make them more marketable.
Further, being moved from one location to another stresses a plant. Dealing with the stress and trying to maintain fruit can be too much for a plant and can kill it. Beyond this, the fruit it would have produced, had it not died, would have been of poor quality due to the fact the tree is under so much stress from moving.
In the future, when buying fruit trees, look for ones that are not fruiting when you buy them, as these will be healthier. If they do try to produce fruit the first year, remove the fruit so the tree is better able to focus on establishing itself and growing healthy. Better to wait a year for fruit and then get fruit for many years to come than to risk the death of a tree for what will be poor fruit the first year.