Will not start and battery light is on

Car won’t start (had been sitting for 5 months) due to me being out of state during that time. Alternator had oil residue but was deemed good still by AutoZone so as recommended, it was cleaned before I had the battery fully recharged at AutoZone. I placed the battery back in and the car wouldn’t start, so I tried to get a jump from a friend’s car but even after revving and waiting it still wouldn’t start. The engine would make a noise, shake up the car, and lights would flicker. When we took the cables off both batteries I tried to start it one last time without any jump and this time no engine noise developed just a clicking noise until eventually no noise or lights flicked. I have warranty on the battery but I believe they deemed the battery good in terms of solemnly voltage. Not sure what it could be as a woman I sadly know very little about the specifics.