I'm not understanding,,,,, Are you saying the starter motor turns the motor over but it doesn't start? (I think "won't turn over" as not cranking on the starter)
If it's cranking over at a normal speed but doesn't even try to start, here's what I would look for;
Tach Movement? - does the tach needle move up slightly when cranking? (now here, on an '01, you are Supposed to see tach movement if you don't have a Trans Temp Gauge in the cluster and won't see it if you Do) This is how you test for a bad CPS..
Does the WTS light come on? (shows the computer is running)
Is there fuel in the fuel bowl now? Does it refill after cranking? (open the drain level to check)
Could the fuel gauge be giving a bad reading? (are you close to empty?)
Is it cranking fast enough? - it won't even TRY to start if cranking really slowly.
Is your truck "chipped"? If so, remove it as a Test.