I have had my Rhyme for quite a while now...and have not had this problem before. I use my dock station all the time, and I have had no problems with it NOT ringing or having the alarm sound through the dock. All of a sudden, out of the blue, it wont. It just rings out of the actual phone, when sitting in the dock. I have checked my settings and it shows that it is paired with the dock (when off the dock) and is checked in the options to use for phone audio and media audio. I have all the volumes turned up as high as they will go. When I sit the phone on the dock, it changes the screen to the landscape one with the time and ability to play music. I have noticed that when I place it on the dock, it does not show a message that it is "connecting to bluetooth" (like it use too) and it does not show "disconnecting from bluetooth" when I pick it up. I tried restarting the phone and it did nothing.
How do I get back the ability to hear the phone ring and alarm through the dock?
for me, my phone started that way. I noticed that it was "paired but not connected" i notice that you said that the phone was "paired" but you didn't mention connected. Try this: go to settings, tap on wireless and networks, tap on bluetooth settings, then tap on "HTC CR M540" (that should be your dock), or you can press and hold and tap connect, or "Options..." and tick the Connect box. *If it is connected, go to options and under profiles you can choose phone/media, you should select both for alarms/ringing.
HOPE THIS HELPS