Bad Battery vs Bad Starter

Friday: Started my vehicle, but had problems. Sounded like battery had 
charge problem, but started anyway.


Saturday: Tried to start vehicle. Turned over but battery died. Later
tried 
charging battery in evening with "smart charger." Before the charger, the 
whole eletrical system would shut down, but the CHECK ENGINE light would 
come on when the door was open. (It's a 94 Ford Aerostar - Other groups
are 
dying) Now I have the charger going on the battery it no longer does that.

Sunday Battery dead again, Charge again. Tried to start again. Nothing. So
I 
asked a neighbor to help me and try a jump start. Still nothing coming
from 
starter. So what I did was test the start relay and jumped the terminals. 
Nothing again. Not even a spark, even though I did put a meter at the 
opposite terminal and grounded it to see if I got voltage when I turned to

the key to the START position.

I did try jumping the terminals at the starter this morning, but got
nothing 
because the batter was dead.

I still need to try to jump at the starter again.

So I am wondering bad battery or bad starter?