The only reason I say this is because the truck wouldn't start a few weeks ago in exactly the same manner. I towed it to the dealership, they charged the battery, and it started up fine for them. The tech suspected HPOP, but he ran tests on it, and after all the tests he concluded that it definitely wasn't the HPOP. He tested it cold, then ran it for a while and tested it hot, and he said it was working fine.
How hard is it to get in there to replace a HPOP or the seal that commonly fails?