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!
You will NOT be able to swap for the 8700 but you WILL be able to swap for the 7700 with no issues what so ever, literally on boot-up the system will immediately recognize the new CPU. The 8700 is a 6 core chip and they don't have any EFI to support that with the current OS. The iMac Pro doesn't even use the new Coffee Lake chip, so it may be doable in the future, but not as of yet. BTW, the latest iMac Pro uses Xeon chips for multi-threading and a kick-ass GPU, so that one will be upgradeable in the future. Hopefully, Apple will come up with some OS updates and the new 8th gen Intel chips will benefit.