2002 Chevy Cavalier hard to start(crank over but no start)

so I bought a 2002 chevy cavalier off my uncle knowing it had an issue.. it was hard to start.. so this is what is happening... it cranks over but does not turn on until about 15-20 times of turning the key and letting it crank for about 3-5 seconds then it was it starts to turn on, as it starts to fire it dies, then after about 2-3 more key turns then it fully starts and runs fine.. no idle problems or anything... I can hear the fuel pump kick on, the starter is good, spark plugs were replaced a couple of days ago( one spark plug was cracked but wasn't the issue), so I'm lost at this point... could my fuel pump be loosing prime?  the reason I ask is because when it starts I can turn it off and start the car back up no problem for upto an hour or two..anything over that it becomes harder to start as the time goes by (example a day to a week of not being turned on).. so I'm not 100% what the actual problem is when it comes to starting the car... like I said everything seems fine other wise... its just the long duration it takes to get it actually started even though its cranking over.. what is it?