How come my car (1996 honda accord lx) cranks but won't start but then later when I try again it starts up?

I try to start my car up and it just cranks and cranks but doesn't start up. I was at it for 30 minutes turning the car on and off and it was just cranking alot but not starting. I don't think its the battery because i jumped the car and tried starting it up and i got the same results (just alot of cranking), so i just give up but then an hour later when i come back and try to start it up it works! The car starts up. Does anyone know what could be the problem? Why does it do that at times? Its like it works at times and other times it doesn't. Oh and i noticed this problem has been occurring more when it gets cold out like during early mornings.

Bad PGI relay

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