If you think putting your car key through the washing machine is bad...

[Ian Key]

I was told by the famous R F Potts of Derby, who are a specialist of computer electrical and electronic components and equipment, that the main thing when replacing these sort of batteries is not to touch both sides with your fingers at once and if possible use plastic tweezers so as not to partially discharge them.

 

[decrep]

I suspect it was the dent in the battery that did for it.
But don't trust that fob for a while, getting run over may have caused a partial short somehow, and could flatten the new battery as well.

Leave it at home for a week and use the spare, If it still works after that, it should be fine.

 

[Rolfe]

Thanks for the tip!