One of the reviews mentions “Fried our vacuum”.
Have you tried going back to the old battery to make sure it can still start-up/run properly?
One thing I would do is check the voltage and polarity on the new battery compared to the old one. So if you have a basic multi-meter, check that.
Though I would think a bad battery would not work at all or worse, break the vacuum like it did this particular reviewer.
I would not expect reverse polarity would work at all, probably trip the battery safety circuit immediately (that it has hopefully).