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Question: Honda civic '96 electrical problem

mfellas, I hope this is a simple question. I am not new to cars but far from a mechanic. I own a 96 Honda civic with an old battery. Never had any unusual problems with car. I had to ship car from oregon to ma on car carrier this caused my alarm to go off until car battery died. When carrier got car to mass he jumped with jump pack and drove car 50ft to driveway then shut off. When I got back to mass battery was dead but jumpable. I got started once let run for 5 minutes shut it off.( I know not long enough) then I put car in storage for about 3 1/2 months went to start today it's dead(I figured that) so I had cables and an SUV. Mows when I get confused I hooked up jumper cables(properly of course) nothing not a chirp or light nothing. Car was running perfect other than obvious battery issue. So can a battery be so dead that when u try to jump it won't even light up dash or dome light or nothing? (I guess i should have added this to question. everything was clean well maintained and hooked up properly. Car has factory alarm that has kill switch if you do not deactivate alarm with remote not key it will not do anything except set off alarm when u try to start. could battery be so dead that with jumper cables hooked up it wont receive signal to deactivate thus not allowing anything to start? this car is meticulously maintained Or could it be more serious and How?? Appreciate any help. Thanks