There's like 3 different problems in 1 thread. What's the primary problem of this thread. I ask that others with a different problem other then the title entails start a new thread so we can properly asses what is what.

For the modules not displaying. This is an itemid issue. The only factor in module display is itemid. That's it. That is the controlling factor. Ensure your itemid of the link (as shown in your address bar) matches that of the menu link you used.

Itemid grabbing code such as clicking a users name in the userlist or say the avatar within the login module checks the database for the itemid. If you have multiple copies of the same link. That is where you're going to run into trouble. As the modules will ONLY show IF the itemid matches that of the menu link you created and assigned the modules to.

So what that means is you might have links in your trash or have other links leading to comprofiler on other menus.

You should have only ONE link going to each component and never more then that IF code based itemid grabbing is used. In this case it's heavily used by CB and having more then 1 link will confuse it. Sometimes it'll grab the link with the proper itemid. Other times it won't. You can also fix this by assigning the modules to BOTH links so both itemids will display the modules.

If none of the above works then delete the menu link, empty menu trash, clear cache, and create the link again.

If you're using 3RDParty SEF then purge your re-writes and let it re-write with the new itemid. Also ensure your sef is NOT stripping the itemid.