94 Lexus ES300 Starting Problem

[starry012]

Hi,
A couple days ago my car wouldn't start (it would make a noise like it was trying to start) but wouldn't start. I then checked the battery (which I just got this past year) and it needed to be recharged so I charged it (but it charged fast so that indicated I might have a bad or dead battery) I then tried starting it after it was charged and it started on the first try but it sounded like it had trouble starting. Later on that same day I tried starting it again and it wouldn't start again but it was making the sounds like it was going to start, and then on my third try it started but my car was making this really wierd sound and then I looked at my dash board and my low oil pressure light, battery light, and check engine light were all on ( my check engine light has been on for awhile now and brought it to a Lexus dealership to see why and they said it was the O2 sensor-so I haven't replaced it yet). I then turned off my car cause I didn't think I should try driving if all those warning lights were on and then I turned off the ignition and got out of my car and it sounded like my car was still running (the keys were out of the ignition) and it just did that for like 30 seconds and died... ( I didn't know if this was the battery discharging or something? why would it still run?)
So, I didn't start it again and since it was a weekend I was going to wait till Monday to either bring it to a dealership or whatever. So just yesterday I tried starting it again to see if I would have to get it towed or if I could drive it... and it started just fine with no warning lights on. I then turned it off and turned it back on and then it wouldn't start again until like the 3rd time I tried. I then brought it to Autozone to checck the battery and the alternator and they said both were fine. So I don't know what is wrong could anyone give me any suggestions as to what might be wrong and if I should bring it in???

Thanks,
Amy