Chevrolet: Battery/Alternator electrical problems, chevy cavalier, battery terms

Question
I have a 1993 chevy cavalier, about a month ago my car wouldnt start, so I replaced the battery in it. It worked for about a month then all of a sudden one day my battery light came on and stayed on until I rev'd my car at high rpm's. I went out and bought a new alternator for it and installed it. My car worked fine for about an hour, then it started doing the same thing again. It will jump start and run fine without any electrical accessories running, but when the Lights, Heater, Stereo Etc.. are on, it has trouble running at idle, but when the accelerator is pushed it quits, but after awhile of running the car will eventually die. When I turn the key on (Engine not running) my lights,and stereo pulsate. (Flash on and off). (Note) I have a Stereo system installed, but every connection for my system is correct.
Please Help me.  I need my car back.
If you could Please email me the answer to my problem

Answer
Hea Brian;
        Well the first thing is the alt. putting out a charg ? did you put a volt meter on it to see what it is putting out , try the battery and see what the alt. puts out also. this will tell you right away if it is charging from the alt. also check the battery terms. and conections on the frame etc. and as far as the stereo try to remove the fuse from it this way you can see if it is from the stereo hook up.and if all is ok than I wonder if there could be a short from the new stereo or someplace else.
get back to me if you must ok.
Happy holidays & Good luck !
Roger