Coupla things,,,, during the '01 production there was a major update to the electrics and that upgrade changed the Instrument cluster to one that No Longer shows cranking rpm on the tach. Next, no,,, this engine will start and run (although very roughly) on just 4clys.
Exactly what codes are you getting, and what is it you'r using to retrieve them?
Give this a try, plug in the block heater for 3hrs and see if it changes anything.
When starting, we want to know that these 4 important values are
As You Crank on the Starter;
1- ICP pressure
2- IPR %
3- RPM
4- System Voltage
And finally, my usual No Start list (I know you've covered some of it already

)
WTS Light? - do you get it when you first roll-on the key? (shows the computer is running)
Do you see cranking rpm on the Tach? Can you verify cranking rpm signal with a scanner of some sort? Do you have a spare CPS to try?
Is there fuel in the fuel bowl now? Does it refill after cranking? (open the drain lever to check) Look above the pass ft tire, you'll see a 3/8" metal tube, against the motor that ends there, it's the drain for the bowl (yellow lever you slide to the side). Get a cup, open the lever, drain the fuel bowl, look at the fuel, close the lever. Then, turn the key to the ON position (should hear the pump) for 15 secs. Drain the fuel bowl again, whaddya got?
Can you hear/feel the pump running (below the dr seat, against the framerail)
Could the fuel gauge be giving a bad reading? (Below 1/4 tank?)
Is it cranking fast enough? - it won't even TRY to start if cranking too slowly.
Is your truck "chipped"? If so, remove it as a Test.
You can unplug the ICP sensor, as a Test, so the PCM sets a default value for the IPR to run on (expect this to set a new "Low ICP" code, don't let that misdirect you after a scan).
Did you check the plug and sheet metal nut going to the IPR? That nut can vibrate off and allow the solenoid going over the valve to slide around. The wires going to the IPR can get brittle, crack, and short together. Make sure the plug & wires look in good shape.