2002 Ford Explorer

When it wont start, what does it do? Click? Nothign at all? Starter engages and cranks engine it just dont turn over?

Do all warning lights come on like normal and fuel pump when vehicle wont start?

If its the neutral safety switch it wouldnt crank at all. When it wont start check the fuel pressure and teh presence of spark. Let me know what you find.

You said it "cranks but won't turn over" - that's two terms for same thing to a mechanic. Ya, nuetral safety switch sounds good - don't know why jumping would help, though. This symptom sometimes occurs with poor connections, check at block and starter too not just at battery, a tight connection's not always good - a "voltage drop" test will show problem - very easy to do if you understand it. Either do some testing or replace it and go from there(or just put it in nuetral) The CEL is likely the DPFEGR sensor - there's a TSB - if it's "tube mounted" it just sticks on top of the two rubber tubes - simple to get at/change.