Make sure the TinyMCE editor is displayed in the Default WYSIWYG Editor field on the Global Configuration page and save the changes at the top (GC page has to have a 'writeable' status though).
Once saved, go back to your module and the editor should now be available to you.
I personally found the JCE editor (and some free plugins for docman etc) much better though.
Best of luck...
Click on "User Manager", then click on your username. In the right panel, check to see that it is either set to the default "Select Editor" or "TinyMCE WYSIWYG Editor".
Also check Mambots>Site Mambots to be sure TinyMCE is published.
For what it's worth, I have had some small problems with TinyMcE in the past myself, I downloaded and installed JCE and bingo, I was up and running again.
More functionality to boot.
Cheers