Long story, please help?

I have a 93 civic lx sedan auto bone stock 130k. my back up car I call it. But lately it has not been so reliable. It worked fine for 1 year and a half. but my car now has a mind of its own. it will just not start out of the blue and if you jumpstart it, it will work fine for a few starts, even a few days. it drives normal but once I turn it off it will either start or mysteriously die again when it wants to. when it dies it still cranks normally but just wont turn over. sometimes when I get tired of it I just let it sit for 4-5 days to a week with the alarm on. when I start it up it suddenly starts up fine like nothing was even wrong with it. It has come to my conclusion that it couldnt be the battery or alternator because I could still start and drive the car without a jumpstart. but if I really need to use the car I just jumpstart it and it works fine.

Anyone have this weird problem before? Should I get the alternator and battery checked. When I bought the car I was told it had a new alternator put in and the battery looks as if its still fairly new.

No CEL have been found.

 

i would go ahead and check the ALT and battery for now but it sounds like there maybe more to it then that... but check them and see what happens