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First, remove all the spent flowers. With some pruning and with proper care, you could easily see flowers then, but they don't usually bloom until a little later. You will have to simulate warmer conditions and longer light intervals, and it is likely to reach your goal here.

This article will give you more information on their care: https://www.gardeningknowhow.com/ornamental/flowers/campanula/growing-campanula-bellflowers.htm

Likely, overwatering! Though it may be warm, it will be important to let the soil dry, very thoroughly, down to about 3 inches between watering.

It will be good to deadhead flowers to promote new growth.

Here is an article that will help you with their care:

https://www.gardeningknowhow.com/ornamental/flowers/campanula/growing-campanula-bellflowers.htm

That is a Campanula. They are very hard to distinguish among the species of Campanula, so the Genus is likely as close as you will get.

Here is an article for more information:

https://www.gardeningknowhow.com/ornamental/flowers/campanula/growing-campanula-bellflowers.htm

Under normal circumstances, they don't bloom during the first year. I would expect to see flowers next year!

Here are a couple of articles that will help:

https://www.gardeningknowhow.com/ornamental/flowers/campanula/campanula-propagation.htm

https://www.gardeningknowhow.com/ornamental/flowers/campanula/growing-campanula-bellflowers.htm

It is not dead. Those look like seed pods forming. It looks like a creeping variety that I have too and it only blooms once in May or early June. Try trimming it back about an inch and see if it will rebloom.

Can you plant it outside? It makes a great groundcover. I have mine in a container outside on my porch. It pretty much is evergreen all winter.

https://www.gardeningknowhow.com/ornamental/flowers/campanula/growing-campanula-bellflowers.htm

This is Campanula poscharskyana, or similar.

https://www.gardeningknowhow.com/ornamental/flowers/campanula