I've had this happen to me a long time ago, when i was playing with conversation ui files.
what I would do:
1. reboot device
2. restore a backup (if you have it make sure it was a working backup, otherwise download from here http://wiki.maemo.org/Conversation_Mods) of the html folder in rtcom-messaging-ui (css, html and js files) close all conversation windows and conversation app. open conversation and see if it works.
3. installed any new apps before this went wonky? try uninstalling them... alhtough i don't know of any apps that'll do this.
4. use default theme and reinstall hildon-desktop (won't be this but would rather be sure before flashing)
5. flash kernel, in my experience solves a couple of these types of problems.