crank and turnover means different things to different people. if it cranks, and cranks anywhere near strong, it is not battery/starter related.
no way to tell what it is if it cranks fine and doesn't start without testing.
could have no spark, no pulse, no fuel or combinations thereof.
could be a coil, distributor, or coil pack (year?), crank sensor, fuel pump, computer, ground/short, and many more.