The persistent storage solutions will only work on 3.0 devices in this case, which will not include the FR235. The best solution I can think of for your situation is to save the time that the application was started in the onStart() method, and add a way to display this time in your application. If the application was shutdown, the user would have to start it back up if they wanted to hide the fact that it was. Doing so would generate a startup time more recent than when they received the device.
Since you are writing things to a log file (Sys.println()) couldn't you just write a line with a timestamp in onStart() and onStop(), and with the log see if two onStarts are called without an onStop in between?
