Engine has all power it needs but won't start

I started my car 1 day and ran inside to get
something when I came back out and my car was
off but all my light and stuff are working so I tried
to turn it on but it wouldn't turn over I proceeded to
jump it but no luck so I replaced the battery with a
new 1 and still no luck so I had the alternator
tested and it  was good so we had someone hook
a machine up to it and it said the fuel pump was
bad so we replaced that and it started up but then
died again and won't turn on no more.. What would
be causing my engine to turn off like that?