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I would leave them uncovered as they are and see if the increased light sends up better shoots.

Sure, but they won't re-bloom again until next year. As long as they have a range of temps from 35-45°F for 12-16 weeks, they will bloom each year. However, indoors it will not fruit unless they are chilled for dormancy, manually.

These articles can help you to plant and care for tulips:

https://www.gardeningknowhow.com/ornamental/bulbs/tulips/tulips-care-and-tulip-planting-tips.htm

https://www.gardeningknowhow.com/ornamental/bulbs/tulips

A sensitive approach must be used during the separation process of 30-year-old tulips evolved into a maple tree because this operation requires protection for bulbs and tree roots. The latening of summer and earliest fall provide optimal conditions to conduct this task when all tulip leaves have withered down. The storage of adequate energy by bulbs during this period supports them for the following growing season.

A small hand trowel and gentle soil excavating around the tulips should be your first step while watching out for tree root damage. The tulip bulbs exist at a depth of several inches below the surface therefore handle them carefully when extracting them yet keep the large maple roots undamaged. Do not break the tight connection between bulbs and tree roots if they are found intertwined with each other. To prevent damaging the bulbs it is advised to wiggle them loose or to delicately brush away excess soil.

Check for damage and signs of rotting on the separated bulbs. Place healthy tulip bulbs directly into a well-draining sunny position situated at a safe distance from the maple tree's feeding and water territory. Surface application of compost on fresh planting areas enhances the quality of the substrate.

I don't see your location listed, but tulips are often treated as annuals because they don't reliably return unless your climate is perfect for them. Certain species tulips have a better chance of returning. You can try planting them in the ground, but your best bet will be to purchase new bulbs in the fall.

It's also possible the bulbs rotted in the container. Here is more:

https://www.gardeningknowhow.com/ornamental/bulbs/tulips/tulips-bloom-every-year.htm

https://www.gardeningknowhow.com/ornamental/bulbs/tulips/tulips-care-and-tulip-planting-tips.htm