1990 Nissan Maxima

Well I had just bought this car from someone recently. And thus far ive had a few problems.
First the battery in the car wasnt even the right one that belongs in their(boguht a new one) Then after doing that the car woudlnt start after it has been started 2 times after that. After researchiung the problem I foudn it was a bad alternator I had the guy come out take it out and go replace it *it was still under warranty* Then the car was running fine until me and my room mates took a drive across town. The car started shaking and what not and I decided to pul into a parking lot. Sure enoug after I killed the engine and tried to resatrt it, it woudl not start. We looked into the engine to find the alternaotr belt broke. Ok no big deal cost about 10 bucks to repalce and was semi easy with a alligator grip wrench. And sometime and alot of dirt. Well its been 4 days since we repalced that and the car has been driving realy find. We went out earlier today to pick a vaccum up we got home with the car having no problems. But as I was heading out to pick someone up I tried starting the car. And nothing is hapening. The engine isnt trying to turn over or anything. The liughts all work and when I try starting it nothing dims. We lifted the hood and listened while it was trying to be started. The battery lets off kind of a hummimg/humming noise that alsts maybe about 10 seconds then stops and wont do it again until about a minute or so*when trying to start* and the right side of the engine has a clicking noise that is heard while turning the key. Weve tried to start it while hitting the starter with a peicie of wood and it wont start still no turn over or anything. So if anyone who knows what the asnwer is to this can u please get back to me realy soon cause this is our only car and is much needed for work. Thanks