On the weekend I sustained an impact to the left two wheels of my car,
enough to pop airbags.

I drove home, and the next morning the car would not start.  I jump
started it, with all the precautions, and drove to a destination.  At
the destination, the car would not start again, and could not be jump
started.

There is only a relay click when trying to start, the windows don't
work, but the locking still does.

I am trying to find out if its a safe bet to fit a new battery myself,
and avoid the hassle of having the car towed in and checked.