There is no error code that is associated with a check engine light that can tell you that there is a fuel pump problem. So find out what the exact code was (format: “P0123”) and post it.
They may have pulled something like a lean condition code (e.g. P0171 or P0174 or both) and then checked fuel pressure or something. Or there are a few codes that would lead one to suspect a fuel pump problem. And then they would check the fuel pressure. But if they did actually find the fuel pressure too low then they probably wouldn’t have told you that they couldn’t find any problem. So, nothing that you’ve said really adds up. Find out more about what - exactly - they have done and tested and how.
Off hand, my first thought was that you have a bad idle air control valve (IACV). This can make a car stall when you come off the gas pedal (which you might do to take a highway ramp), and can make it start, run for a second, and then die immediately.
But it could really be any number of other things too including a failing fuel pump. I have no idea why this shop would be “flummoxed.” It’s not that hard to find out. Did they check for spark? (How old are your plugs and wires? ) Did they actually check the fuel pressure? (How old is your fuel filter?) Did anyone try to keep it running by using some starting fluid in the intake? Did anyone try to keep it running by holding down the throttle some? (This would compensate for a dead IACV).
So anyway - a car that won’t run is a very basic - perhaps THE most basic thing for a mechanic to sort out. If you want help remotely report more about what has been done and why it seems so difficult.