I agree about the charger first, if it isn't below freezing, batteries generally
withstand discharge. You can pop the cell covers on top of the battery and make sure the electrolyte is up and the plates are NOT exposed, if so, add ONLY
distilled water that you can get at any drug store. Don't use tap water.
Get a battery hydrometer/checker at a car parts store and you can check the specific gravity of each cell. That's the way to tell that a battery is junk.

However if the car doesn't crank with Jumper cables, that indicates that the cables and connections have a problem.

Start by getting a battery terminal wire brush and clean the battery and cable connections so they're shiny clean, then apply some grease, dielectric silicone is good.

You can check the connections to the starter and the ground connections as well.

Everything needs to be hooked up without corrosion to carry the high current flow
necessary to spin the starter.

Get an VOM to measure the charged battery is 12.6VDC and with the engine running see about 14VDC charging volts. If it stays at 12.6 it means the
alternator isn't charging the battery. (Which still can be a bad cable connection)

Bill