If these are violets:

1. Not flowering for 6-9 months is not necessarily a problem; not flowering for 12 months is a problem. The latter might suggest not getting a cold spell in winter, having too much nitrogen or not enough potassium, preventing the plant from experiencing lengthening days, and too much/deep shade would not help.

2. Sickliness after splitting a crown: How much good root was left on the piece which is poorly? Does the scar where it was split look healthy or it is rotting (with/without woolly fungus)? Has it been overwatered and/or given too rich and poorly-drained compost? Has it been in too much sun since splitting? The behaviour of the leaves suggests the plant has not re-established its sap stream - which can be due to one or more of the aforementioned factors. It might be difficult to save it now, but if it still has some good parts, treat it like a cutting. That is: cut it back to sound stem tissue, cut most leaf blades by about 75% (to reduce fluid loss), dunk in fungicide, plant in open 50/50 sharp-sand/peaty compost and keep in a partially closed container in good light but out of sun. Whether that rescue will succeed depends a lot on the species you have (many far eastern species root fairly well from pieces of root) and on luck!