Q: Starting problem

My car's been having some issue with starting for some time. In the last 6 months, I have gotten a brand new battery (2016 summer) and a new starter (fall 2016). I live in Philly and I'm assuming the cold weather has somewhat of an effect but what surprised me was that one night the car would start with no issue (granted on a second try/turn still pretty strongly; however the next morning the car's battery would go completely dead and not start at all. I tried to get a jump start after charging for 30 minutes which charged the battery which we could tell with lights and (sound) turning over more and more but still not enough to turn over completely to get the car going. If the problem doesn't lie with the battery and starter, does it lead to the alternator or could there be other problems?

On a side note, cars been having some random electrical problems especially with the E-break light coming on randomly even when the break isn't on.

My car has 90500 miles.
My car has an automatic transmission.