The TinyMCE editor makes it very difficult to include Google Adsense code in your articles (you have to turn off the TinyMCE editor, insert the code, and then never edit that article with the TinyMCE editor after that).
At first, I was infuriated that there was no HTML button on this editor at all! After poking around for about a half-hour, I figured out that you have to go into the Group settings under Components...JCE Administration, click on the "default" group, click on "layout", and then drag the icons for HTML editing into the "current editor layout".
So for all of you who are confused by the lack of an HTML button, it is there, you just have to configure it, and the configuration is VERY well buried in the settings.
Hope this information is helpful to some of you.
Unfortunately the no-show HTML / AdvCode button is due to a bug in JCE Admin Component 1.5.1
This will be fixed in the next update.