03 sunfire wont start

I have a 2003 Sunfire. I am having a problem with it. I drove it the other day, got out, went into a store, came back out and started the car. Well, it started and shut right off. I tried starting again, and it wouldn't even click or attempt to start. THere was no power at all. Well, about a minute after this, the car beeps a few times as if the power was turned on. I tried starting it and it started up just fine. Well, about a week after this, I was driving and noticing the speakers I had put in over 6 months ago, was fading on and off. I got home, turned off the car and tried turning it on, and it did the same thing. Well, i went in and did some things came back out and it started up just fine. What in the heck is going on? Is it something to do with my speakers/amp? I am a female, so I don't know anything about cars. My father took it to test the battery, and that wasn't the problem. I have an appt to have it looked at, but I just know they aren't going to find anything, since it rarely happens. HOwever, something must be wrong or it wouldn't be doing that. I just wonder if the speakers are running something down or maybe it's something completely different. Does anybody have any ideas, I would reaally really appreciate some help!! Thanks so much!!!!!!!!

i had this problem a couple years ago with my car.. i think it's the same thing.. check the connection to the battery, from the amp (i think).. what happpened in my case, wuz the guy that installed my stereo, didn't tighten up the connection to the battery, like on the plugs.. so the car wuzn't getting the full juice from the battery, even though the battery is fine.. :)..