After one week of water deprivation, only dead roaches will remain. The others will have left your dwelling to seek water elsewhere.
Wipe your sinks dry. Keep dishes, cups, and food containers clean and dry. Surround drains with dry, powder silica gel. I bought a five-pound container of the plain powder on Ebay. Other places sell it mixed with color-changing indicators, and in little packets. Diatamacious earth works, but can be harmful to humans. The point is this: If a roach crawls in it, the roach will soon dry up and die.
If you are living with bed bugs, seal your mattress and surround your bed with silica gel. The bugs will sense the carbon dioxide you exhale, walk throught silica gel, and dry up.