Car starts when it wants to! Help! Options

[Por2geezcelica]

Hey guys, need your help with this problem im having. Currently my car is starting when it wants. This is what is happening: I turn the key and all the lights on the dash will dim and the starter will click once or twice, but wont do anything after. Sometimes when i bring the key back the lights will stay dim as if theres not enough voltage coming from the battery, and other times when i bring the kay back the lights will light up normally. This happened yesterday. I changed out the battery today and it started up fine, then later on in the day it did the same thing with the new battery so it isnt the battery. I changed the starter a few months ago, but im thinking this may be a starter problem since i believe it was a refurbished starter. The only thing is that sometimes when i bring the key back and am not trying to start it, the lights will stay dim as if the battery is not delivering enough voltage. Could a bad starter cause the lights to dim when not trying to start it?

I have narrowed it down to either the starter, maybe a bad ground point, or maybe the battery cables or the connection to the battery cable terminals? Let me know what you guys think.