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Saving the tree, really, depends on if the tree is still alive or not. If you scratch bark and see green then you have a chance. This cannot be controlled by your are anyone else, though. With proper care the tree may be able to survive, but this is no guarantee. These articles will help:

https://www.gardeningknowhow.com/ornamental/trees/tgen/what-does-a-dying-tree-look-like-signs-that-a-tree-is-dying.htm

https://www.gardeningknowhow.com/ornamental/trees/weeping-cherry

I can't tell if it's in a pot or in the ground, but weeping cherry trees in containers don't live as long as those planted in the ground. The lack of blossoms is usually an environmental issue, such as a drought or late spring freeze. Make sure the tree is still getting good light and is watered when rainfall is lacking. You can also check for pests on the tree. Pruning dead and diseased wood will invigorate the tree and may help. Also make sure it is not getting excessive nitrogen, which will sacrifice blooms. These articles should help:

https://www.gardeningknowhow.com/ornamental/trees/weeping-cherry/pruning-weeping-cherry.htm

https://www.uvm.edu/~pass/perry/oh40.html

https://www.gardeningknowhow.com/ornamental/trees/weeping-cherry/weeping-cherry-growing-tips.htm

https://www.gardeningknowhow.com/edible/fruits/cherry/cherry-tree-diseases.htm

https://www.gardeningknowhow.com/edible/fruits/cherry/how-to-water-a-cherry-tree.htm

It does sound like there may be an issue. I wouldn't discount the tree just yet. They should start showing signs around the end of April into may, so it could still be trying to break dormancy. I would snap a twig on the tree and make sure that it has some give to it. Green can indicate a living branch, as well. If all branches are brittle, then it may be a lost cause.

This article will offer more information for the care of the tree:

https://www.gardeningknowhow.com/ornamental/trees/weeping-cherry/weeping-cherry-growing-tips.htm

This can be quite complicated, as there are many factors that can contribute to this issue. Unfortunately, your photos did not come through. I am unable to rule anything out, or narrow it down to anything specific. This seems like some sort of disease, however. The sucker formation near the base is likely due to stress. I would not let that grow, since it is likely the root stock of a different tree in the same genus.

Treatment will depend on the specific disease. This might be best diagnosed with your local extension service:

https://duckduckgo.com/?t=ffab&q=horticultural+exrtension+search&ia=web

This article will help with the general care of the tree:

https://www.gardeningknowhow.com/ornamental/trees/weeping-cherry/weeping-cherry-growing-tips.htm

Unfortunately, your photo did not come through. I am unable to see the issue in question. If the tree was heavily pruned, then it could have shot up suckers from the root stock of the tree. Essentially, these are a completely different tree than the top grafted portion. Usually, specialized specimens are grafted to more vigorous root stocks to promote faster growth. If the tree is under stress, then it can send up suckers from the root stock. Since these are likely an upright variety they will look like the bottom tree.

https://www.gardeningknowhow.com/ornamental/trees/tgen/tree-sucker-removal-and-tree-sucker-control.htm