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It sounds as though you may need to fertilize and, perhaps, change the location of the plant. Since the Neem oil didn't work, try an insecticidal soap on the underside of the leaves.

Here's an article that will help you review your plant's growing conditions: https://www.gardeningknowhow.com/houseplants/dumb-cane/growing-dumbcane-dieffenbachia.htm

It's hard to tell whether the plant is broken or just bent. Here are two articles that should help. The first explains how to propagate this plant - you may need to do that. However, if the plant is simply bent, it may be repairable.
https://www.gardeningknowhow.com/houseplants/prayer-plant/maranta-prayer-plant-peacock-plant.htm

https://www.gardeningknowhow.com/garden-how-to/info/fixing-bent-stems-plants.htm

I the browning leaves are at the bottom of the plant, that is normal. Just trim those off. If the browning leaves are higher up on the plant, it could be a watering issue.

Here are a couple articles that should help:
https://www.gardeningknowhow.com/houseplants/dumb-cane/growing-dumbcane-dieffenbachia.htm
https://www.gardeningknowhow.com/plant-problems/environmental/what-causes-brown-edges-on-leaves-of-plant.htm

They can be slow growing, by nature. If it doesn't get fertilized every two months or more, then it will likely grow much slower. I would say that feeding them will help to speed them up just a little. This article will help you to care for the plant:

https://www.gardeningknowhow.com/houseplants/dumb-cane/growing-dumbcane-dieffenbachia.htm

Try giving your plant more light (indirect but bright) and rotating a quarter turn regularly, and see if that helps. They are heavy feeders and need fertilizer every 4 to 6 weeks. Also, keep the soil moist but wait till the surface dries out between waterings.

https://www.gardeningknowhow.com/houseplants/dumb-cane/growing-dumbcane-dieffenbachia.htm

http://www.ladybug.uconn.edu/FactSheets/dieffenbachia.php