Can these kitchen cabinets be touched up?
If they have poly on them, they will not accept a stain
It is unlikely that kitchen cabs were just stained, and not polyurethaned or shellacked or varnished in some way
Water damage is a difficult problem to address properly in the best situations
Trying to "touch-up" water damage is usually not possible...but ever so slight and specific water damage might possibly be "touched up"
W/o seeing your specific problem it's hard to tell, but I'd have to say the chances are pretty huge that a strip and refinish, or a paint job would be the solution