With the phone unpaired to any device, does the phone itself receive texts? If so, your Kenwood isn't compatible with Kit Kat for some reason. (And the fix is Kenwood updating their product.)
If not, have you tried any other SMS app? If not, do so. If that works, your text app isn't working right. Install Messaging (free at Play) and use that for texting, or use whatever app you prefer.
If that still doesn't work, bring the phone to your carrier's store and ask if they can reflash the update - the update you got is corrupt somewhere. (It happens every so often.)
Texting uses the same path as voice, so if you can make and take phone calls, the phone itself (hardwre, radios, etc.) is working, as far as texting goes.
