As mentioned, a less ambiguous description of the no start situation is needed. When you turn the key in neutral or park did the starter turn the engine? When it died was it like a switch had been turned off and then all the dash lights came on?

Normally these "dies and restarts later" situations involve seconds or minutes before restarting so yours is slightly out of the ordinary. Is the car a manual or automatic?

Either way, the main fuel pump fuse is the primary suspect if I remember Art B's description of what years had it back in the main fuse panel (should be #6). Towing could have jiggled it enough to make contact again for now. Remove the fuse, inspect the ends, clean and retention the fuse clips and reinstall the fuse. While you are at it treat all the fuses to this and replace any plastic and "tin" fuses with ceramic and brass.

Next on the list is the crank position sensor...again because it seems repositioning and not temperature was the "fix".

There are like three to four more possible suspects but even the least capable mechanic should have noticed a couple of them and we need you better description of what happened because I think your beach ball description is a red herring and is just going to confuse the issue.