Our white-and-silver single-button Roomba, from the pictures I believe a Roomba 530, has been doing the circle dance for a while, and the house is starting to show that we have two running kids and one non-running Roomba, not to mention a black cat and white carpet. Yeah. Time to get serious!
Last night while looking for answers online, I watched the circle dance carefully to match it to the manufacturer videos. I watched our Roomba patiently, unlike usual, for several minutes, and was rewarded with an error code! 9 beeps! Well, that's easy: 9 beeps means the bumper sensor is stuck. You can always start with Roomba's support and go directly to Error 9, or peruse Owner's Guides.
From the RobotReviews post I also learned that diagnostics mode isn't as easy as multi-button presses on this (our second) Roomba. You must have the SCI cable, interface documented, although you can make your own cable if you can get the control software.
Then again, for not much more than the cable costs and from the same source as the needed bumper sensor parts, you can also get repair service. It seems like a pretty good deal so I can get back to playing with my kids and ignoring mundane vacuuming because Roomba does that, although the repair service lacks the DIY goodness of making my own cable. It's been a while since I've done that ...