There should be a set of buttons that comes up to decide what level of analysis you want to do and you can select one of those.
Computer analysis won't work!?
This is what it directs to (Just figured out how to make a screen-shot). Can't find any level options. When I push play it just it replay the game, No analysis. This can't be right?

The buttons show up above where it says Self Analysis. Looks like the browser isn't showing the layout correctly my phone does the same type of thing on the mobile optimized site. One thing you can try is forcing it to load the desktop version (since that looks like the mobile version) and it may help.
Hey chess.com
I can't get my games analysed! I've checked the Q&A's and done as it says, but it doesn't work. When I push the com.analysis-button it directs to the board editor, but the analysis doesn't start. Am I missing something obvious or could it be something technically?