Starter issue

I have a 1996 Toyota Camry. About a week ago my battery was replaced and now I cannot get my vehicle to start. at first there was no noise when i would try to turn it over. After it was jumped it ran fine but died after I turned it off. Then when I would try to turn it on it would make rapid clicking noises. I noticed today that the negative battery terminal was loose. I put it back on and hit it gently and when I tried again to turn it on the lights came on but this time there was only one click. Could this be a problem with the batter terminal? or could it possibly be the alternator or the starter or the starter solenoid? and how would I know what the problem could be without spending money to get it looked at? Thanks Guys

Maybe you should start somewhere back before the battery was replaced. What was the car doing then? Who replaced the battery? How was it determined that the battery was a problem? Was the battery that was installed fully charged?

Somewhere in the whole sequence the battery and charging system should have been tested. So, do you know whether or not the alternator is any good?

Then you also have to worry about the battery cables. The battery end of those cables is one thing and if the connections are now clean and tight you need to worry about the other end - the ground points on the chassis & connections at the starter. If those connections are good and clean and tight then you need to start worrying about the condition of the cables themselves - hidden corrosion underneath the sheathing and such.