97 e150 van 5.4; engine only starts by jumping the solenoid but not with the key.

If you jump battery positive to solenoid terminal s the starter should kick in and crank, if not run a separate ground from battery negative to solenoid base if nothing changes check the neutral safety switch with a test light (not a voltmeter). I hope this helps. Take Care.

Could be coil/module, crank or cam sensor.

Check the small wires going to the starter solenoid. Hook up a voltmeter on the wires and see if you have power in the crank position. The ignition relay may be why power is not going through the keyswitch. The fusible link, probably not a problem if the engine runs.

If you have an automatic transmission you need to check the neutral safety switch; if it's a manual check the clutch safety switch.

Put key in the ignition,take it out of park and into neutral,wait few seconds,put it back into park and should start up.

I'm not positive the wiring is the same for trucks and vans, but you should have a yellow wire for both relays that go to a fuseable link off the starter solenoid. The key switch powers the EEC relay on, and the computer grounds the fuel pump relay on.
You may want to check the fuseable links and power coming from the key switch.

It may be the coil pack

the heater core is located in the black box that is in the pictures (see below). To get access to it, you will need to remove the blower housing. The blower housing will separate from the main HVAC box, and will give you some space once it is out. Then we need to wrestle the main box loose from the firewall. That means dealing with the A/C pipes, heater hoses, vacuum hoses, mounting stud nuts under the hood and mounting bolts inside. Once the box is moving, the dash needs to "get floppy" so you can pull back the passenger side far enough to give the main HVAC box enough room pull away from firewall, and to "roll" back towards you. At this point the heater pipes will be visible, and the cover that contains the heater can be removed. It's a big job. Your car has A/C. The description in the haynes book is for a car w/o A/C. If you're not comfortable with plastic dash board removal, this job is not for you

The Starter relay is bad.

Disconnect the battery cable ,wait about 4 to 5 hour so that the computer can reset. If the enignee light still come on change the air senor switch, locate on your muffler pipe under the driver side of vechile