Looks like you are getting air in the system somehow. I would start by replacing input side fuel lines to the pump: especially one from metal fuel line to head connection. This is a crimped connection to metal fuel line. You will need to make a lateral cut to cut the crimp sleeve only (be careful not to cut any part of the metal line). Then pry open the crimp with flat head screw driver. Watch or read some articles online on how to remove crimped fuel/transmission line. Replace the line with good marine fuel line and worm bands on both ends. You should also replace fuel head to CP3 pump fuel line just to be safe. If you still get the air the in the system then it must enter from connections near fuel tank. The best solution would be to install in-tank lift pump and replace the quick connect lines near the tank with proper fuel lines and worm band.

Yes, but start from a crimped fuel line going from metal fuel line to fuel head, as I said. This one is easier to replace. The fuel head need to come off. Also replace fuel line going from fuel head to CP3 pump as a cheap insurance. If this does not cure then move to the tank (which is a lot of work to drop).

start from a crimped fuel line going from metal fuel line to fuel head

I didn't mess with undoing the crimp
I just used a small pipe cutter to cut the crimped end off completely.
Then just added my own 3/8 fuel line with new hose clamps.

In my case, the original rubber line was rubbing against a bracket and almost wore completely through.

Also, back at the tank, there is a coupling in the fuel supply line between the plastic line from the tank and the hard line on the frame. I cut that coupling out and replaced with 3/8 fuel line and new hose clams.

Yes.
I just slipped 3/8 fuel line over the hard lines and clamped.

I choose to un-crimp the hard line because there is a little bump on the fuel hard line which allows secure connection. Notice the bump just ahead of the band in this picture:


This is the first line you should start with. Next is the line going from the fuel head to the CP3 pump.

Have the battery tested. If voltage is low then you will get crank but no start. It seems ECU needs full voltage to make all systems run properly.

Any DTC codes in ECU?

much to my chagrin, after changing out all of the fuel lines, I still have a no start condition. I have also added an inline fuel pump. there is a fuel coming out of the fuel filter assembly when the valve is cracked and the key is in the run position.

it appears as though we may not be looking at a fuel supply issue.

the timing belt was replaced 40,000 miles ago, in 2012.

I am open to suggestions as to where to look next.

Crankshaft position sensor is one possibility. Sometimes they go bad without any warning.

Have the battery tested. If voltage is low then you will get crank but no start. It seems ECU needs full voltage to make all systems run properly.

Any DTC codes in ECU?

Just for what it is worth, since you've taken care of air-in-fuel issue, and a fully charged battery seems to have at least temporarily solved the no-start issue, I'd consider the possibility that either the battery is on it's last legs or that you have a parasitic electrical draw draining it.

A couple years ago mine developed such a draw. It would completely kill the battery in 2-3 days, and make it just weak enough it wouldn't start in just over a day. I have yet to figure out exactly what the issue is because it comes and goes. I put an ammeter on it, and see that there is a 7 amp draw that seems to turn on and off at random times, which is perhaps why it is hard to track down.

I finally installed a battery cut-off switch in frustration, and now when I park it for more than an hour or two, I disconnect the battery with the result that it starts every time, even after a two-week stay at an airport parking lot.

In any case, some folks have found that the glow-plug relay sometimes caused a parasitic draw (not the culprit in my case, having replaced it). But you might look for such a draw.

well, it started this morning. how confident are you that it fully charged battery would solve this? by that, I mean permanently solve this.