1984 Toyota Tercel won't hold a charge

We have a 1984 toyota tercel and the battery wont hold a charge or its not getting any thing we just got a new alternator and the battery is pretty new we have no clue what could be the problem. Also when it was running the front turn signals would not work and the back ones would and then the next time you'd turn it on the front would work and the back wouldnt could some one please help !