First, it sounds like it "cranks" all the time, the starter works. The engine only starts when it's been sitting.
So now you know the MAF is bad. If it were working, you would have noticed a difference. Time for a new MAF.
It didn't start with and it didn't start without. That rather means the MAF is not an issue, it's been eliminated. It's likely more a red herring that people are responding to because it was mentioned. If the internal components are fine and just the plastic housing is damaged, it can probably be sealed up with RTV and used.
Cam and crank position sensors don't really care how much gas you give the engine. The previous owner's suggestion of these is also likely a wild guess, and probably an attempt to sell the car as a "just needs a sensor". That's almost a scam pattern I've seen: "just needs an oxygen sensor" = "I'm not telling you the $1600 quote I got for a new mani-cat needed to make the car pass emissions".
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The first thing is to check for common problems. Oil in the spark plug wells is very common in poorly maintained cars, and hot oil seems to short out the spark even better. Do the maintenance of pulling all the plug wires and see if they are wet with oil. Then clean out the spark plug wells, and pull the all spark plugs and inspect. Make sure they are all the same brand (preferably AGSP32FM; AGSP32PP = they're probably old), the same color on the ignition end, platinum buttons on electrode not missing, and gapped uniformly at .44. Then do a compression test on all the cylinders, and see if you didn't get sold something with bad valves, or a blown out ring (which only runs when sealed with fresh oil from leaking valve stem seals).
We need to ensure engine-managed spark is OK, and the next is the spark plug wires. Test with a multimeter, they should all check at 8-16 kOhms. And with that, reassemble and find a buddy. A $10 ignition tester, that you hold next to the wire while an assistant turns the key on your non-starting car, will let you see that the computer makes spark through the DIS and coil for all cylinders.
Then we must investigate likely issues that would cause this particular symptom. My opening suspicion is that there is a fuel delivery problem, especially that the car won't stay running, giving it gas makes it stall. A fuel pressure gauge on the rail, seeing that it maintains 40psi, will let you know if you can eliminate the fuel pump, filter, regulator, etc. as potential problems. Replace the fuel filter anyway as it's likely never been done. Air filter too.
So if we are sparking at the right time, and always have correct fuel pressure, it's down to mixture. There are lots of things to go wrong. EGR valve stuck open, idle air control valve sticky, leaky or bad injector, vacuum leak. Bad O2 sensors + bad MAF would mean the computer doesn't have enough sensor input to regulate fuel. Throw in a throttle position sensor with dead spots and the computer would have no idea how much fuel to deliver.
