A Wheelson that runs happily on the cable but dies the instant you unplug it is pointing at one thing: the battery is not feeding the board. That is usually a connection rather than a faulty battery.
Charge it properly first. Leave it plugged in for a full hour. If the battery arrived empty and has never charged, USB-only behaviour is exactly what you would see.
Check the battery connector. With the casing open, compare the battery lead and its connector against the build-guide photographs at circuitmess.com/blogs/resources. It needs to be seated fully — a connector that is in but not home can pass a trickle and still drop out under the load of motors.
Check the switch position and that nothing from the assembly is holding it between positions.
Do not unplug and re-plug the battery lead repeatedly — check it visually, correct it once if it is clearly unseated, and if the behaviour continues, photograph it as found.
Email [email protected] with your order number, a photo of the battery connector as it sits on the board, and a short video: running on USB, then what happens when you unplug. That pair of clips usually tells us the answer straight away.
The equivalent behaviour on Chatter 2.0 has its own article: My Chatter 2.0 only works when it is plugged in over USB. What should I check?.