You may have a bad control board, so I'd recommend calling Dyson and making use of the warranty. Depending on the serial number, you should have no issues claiming warranty, even if this was purchased second hand. That being said, if you are looking to repair the issue, you must first be sure it is the battery and not some other part.
You can remove the battery and put it on a charger to see, then measure the voltage. I'd make double sure there are no shorts in the board, that should be relatively simple with the help of a voltmeter on continuity setting. Past that, I'd look at the board and see if it does provide power. One thing I have noticed with the cordless Dysons is that some work intermittently based on how dirty the filter gets or if the dirt receptacle is full. That in itself is not a fix, but also make sure the pressure sensor isn't shorted on your unit. I hope you can make use of the warranty, as this is a lot of work which may still lead you nowhere. Best of luck!