What voltage do you measure across each of the (probably two) batteries in it, with the charger not connected, and the scooter turned on? If it's too low, the system probably won't run (see below). If it's normal, it may be damaged. Full is around 14-14.4v each 28-29v total, empty is around 10-11v each 20-22v total.
If it's using two 12v SLA / AGM batteries, it probably barely operates at 20v, and may even have an LVC (low voltage cutoff) at or even above that point, so it's probably not going to operate from the Dewalt battery.
You can still try it, if the DW battery will operate things other than the tools it's made for.
Otherwise, for simplicity, I'd recommend getting the exact same batteries it came with as replacements. Not just any old SLA, etc., but the exact same brand/model for best match, assuming it came with the right ones to start with. You want ones that are "deep cycle" "EV rated", "high current", not "standby use" or UPS batteries, etc. You want ones that can supply high current without sagging in voltage much.
When you get them, don't forget to keep them charged up all the time; letting them sit for any amount of time after using them without recharging them, or just letting them sit and self-discharging over time, is usually what does the most damage to them.