2006 Prius shows P3193, but tank is full

I have a 2006 (Gen 21) Prius that I'm trying to get running for my daughter. I've replaced the traction battery, 12V battery and catalytic converter. It will now run for about 20 seconds, then shuts off and triggers P3193, out of gas. I was pretty sure it wasn't out of gas, but I put gas in from a can until it ran out the fill spout, so I know it's full. I've cleared the codes and unhooked the battery, but the codes keep coming back. The combination meter also went blank, so I don't know how much gas the car thinks it has. I intend to replace the capacitor in the dash at first chance, but I don't really think this will fix it. Anyone know what else it could be?

 

I had a 2 gallon can, and it only took about 1 gallon to fill it up completely until gas started to run out, so I know low gas was never the real issue.

I'll pull the dash and solder in a new capacitor to get the combination meter working. My thought is that this should at least let me see how much fuel the car "thinks" is in the tank. Is this code set just by the fuel level in the tank? I've reset the code multiple times with my scanner, and it just comes back. It seems to run fine for the 20 seconds or so until the P3193 code gets set, so I don't suspect a true fuel or spark issue.
The car has been sitting, and it was in a fender bender on the left front, so I had to replace a piece of the wiring harness with the abs sensor and inverter coolant reservoir connector, but the fuel tank is a long way away from the area where that damage occurred. Is there a resource that will tell us what is the code setting criteria? Is there a separate sensor that triggers the P3193 error, or is it just the same one that shows tank level on the combination meter?
I guess it's time to print out the wiring diagrams and look at the relevant signal(s) with a meter.
I haven't seen this issue before, so any direction would definitely be appreciated.

 

Thanks for the responses, and I don’t want to appear obstinate, but I’ve read post #3, and am having a little trouble understanding how it applies in my case, since even an hour after I reset power, the same p3193 reappears after I clear the codes. Since the engine starts and runs perfectly for around 30 seconds until the p3193 code comes back, I’m not sure how to proceed to troubleshoot a p3191 no start code. Any thoughts on that would be appreciated. If I understand correctly, after power is restored, the fuel gauge has one flashing segment until the computer figures out what the fuel level actually is, then it displays correctly. With a blank combination meter, I don’t really know what the reported fuel level is. Is it possible that a faulty tank level sensor (or wiring) is erroneously reporting out of gas, causing the recurring condition that I’m seeing? My hope is that if I fix the combination meter capacitor, I can at least tell what the reported tank level is, and get some diagnostic direction that way. Am I way off track here? Again, I’m incredibly grateful for the cumulative experience and knowledge of the Priuschat community, and will gladly perform any suggested tests to diagnostics this issue. This is the fourth Prius in my family, and I admire the job that Toyota did designing this remarkable car.

 

Au Contraire, Mon Freres, I can state definitely, positively and unequivocally that the ICE is starting and running 20 seconds or so until the p3193 code is set. How do I know? I installed a new catalytic converter to replace one that was stolen, and I still have a small exhaust leak, so there is absolutely no doubt whatsoever if and when the ICE is running. Also, I’ve had three other gen 2’s with bad combination meter capacitors, and they all ran quite happily with blank combination meters and without setting the p3193 code (until they actually ran out of gas), so I’m confident a bad combination meter isn’t setting the code.
I’ve successfully fixed all three bad mfm’s, and I even bought a dozen of the correct electrolytic caps off amazon so I wouldn’t have to scrounge them from my son’s old cassette players, so I feel pretty confident that I can fix it. This brings us back to p3193, out of gas.
1. I know the engine is starting and running, so to me, there’s no need to further chase down that rabbit hole.
2. When the engine shuts off, it sets code P3193, not p3191, not even once, no matter how long it’s been since the 12 V power has been on.
3. I’ve got gas running out the filler, so I know the tank is full.
Therefore, to me, the condition which kills the ICE also sets P3193, and it’s not because the tank is or ever was empty, or because the ICE isn’t starting.
My working theory is that the computer is getting a false signal indicating an empty tank, which shuts down the ICE after 30 seconds, and sets P3193 code. I can probably find a parameter indicating fuel level using my Autel bi-directional code reader, but I know the mfm capacitor needs to be replaced anyways, so I think I’ll just do that first. If I’m right, then the fuel gauge will show empty no matter the level of the tank, and I’ll need to then replace the sending unit, or fix a wiring problem.

history of the car:
It has about 75k miles, and I bought it for my 16 yr old daughter non-running for a pretty low price. Previous owner said his mechanic had replaced the traction battery, 12 v battery, left fender, and dash, but still couldn’t get it running. (And the mfm was still intermittent). So it sat in a church parking lot for about a year until he was finally told to do something with it. By then, the cat had been stolen, one back door window was broken out, and of course, both batteries had gone bad from lack of charging.
I bought it off Facebook, replaced both batteries, the cat, and the back window, and I’m trying to get it running before the traction battery again fails from lack of use.
That’s it. I’ve got a clean 75k Prius that only runs for 30 seconds before setting the p3193 code, and the intermittent multi function meter is now mostly off, so I don’t know what fuel level is being reported to the computer, but I suspect it’s mostly 0.
Back to my original question: what is the code setting criteria for P3193? Is it low analog fuel level signal, low fuel pump pressure, a discrete low level switch, or something else entirely?
Again, any and all suggestions are really appreciated. In my 10 years or so of owning gen2 prii, I haven’t come across this particular symptom, so I’m scratching my head a bit.

 

Humble pie. Ok, had to consider it a bit to be convinced, but now that I think about it, maybe the ICE only sounds like it’s running, and the exhausty noises are just uncombusted gases being pumped through the cylinders at 1100 RPM running speed, like a giant air compressor. I’ll tackle it again when I get back to the states next week. Thanks for making me reconsider the facts in front of me. I’ll keep you posted.

 

Think I’ll try something new, stop explaining why I think I’m right, and start listening to the voices of experience.
So, what can I get to keep the traction battery charged while I figure out why the ice isn’t starting?