Lexus GS 2006-11 :: GS300 Just Stopped Running After Driving Approx 1 Mile

I have an 06 Lexus GS300 awd. Yesterday, when I left out of my neighborhood, my car drove approx 1 mile and just STOPPED running. I coasted to the shoulder of the road & attempted to start it again. It cranked & started for about 2 secs & died again. After that, each time i tried to crank, it would try & try to start (starter sounded strong) yet would never "turn over". I could feel/hear a few rough spitting & sputtering type feelings/sounds trying to start it, but ultimately it wouldnt crank.

I called a friend (another single mom) to come get me & i purchased some starter fluid & went back to try it. We hooked it up to her battery as I had run mine low trying to crank it. After it had been sitting there while we went to the store, it again tried to crank when I attempted to start ot, but died again within a sec or 2. Then, wouldnt fully crank again. I hear my alternator clicking & as i said earlier, the starter sounds very strong & normal when i push the ignition button.

I tried to just turn it to the "on" position (2 button pushes), leave it a few secs, turn off, then try to crank again (hoping to "prime" the gas lines in case it somehow had sucked in any air or water....which it kinda "feels" like) Still after all that....nothing. I tried having my friend crank while i sprayed starter fluid into the intake, and it actually cranked and would stay running as long as i was continually spraying the fluid. The sec i stopped, it stopped. I really dont hear the fuel pump turning on, although admittedly I guess I never have paid attention before this to know if I ever could "hear" it previously. Im wondering if its just a very quiet one, or if its not turning on at all? (I understand it's in the back of the car kind of under the backseat & not under the hood).