2002 Ford Taurus cut off while at a stop light. Won't start back up?

I got a 2002 Ford Taurus. My wife was driving the kids to school this morning and stopped at a right light. A moment later the car just cut off. Was able to tow it home (thanks triple a). The only issues we have had recently with the car is the battery. It does need a new one. Battery dies quick if lights are left on. We got a portable jumper that works well if the battery dies on us. I don't believe the issue is with the battery since it died while the car was running.

As of right now the battery is working. Windows roll down, lights turn on, ect. There's gas in the car. When you try to turn it over you can hear the engine try to start but it just doesn't start. Sounds like there's no gas to start the car although there's.

Anyone know what this issue might be? What would cause the car to just cut off at a red light then not start again but have the engine sound like it's getting ready to start when you try? Or what I could look for or try to do to find a resolution without taking it to a shop?

Low or no fuel pressure, timing belt slipped? Have it checked for compression and fault codes.

When you turn the key to start, the CHECK ENGINE light should go on. However, while it's cranking the light should go off. If it doesn't, then the computer isn't getting a good signal from the crankshaft position sensor. If it does go off, slap a fuel pressure gauge on it to see if you're getting fuel pressure.

Mom has a 2001 taurus that would stop at red lights too, it wasn't the battery for us neither. The problem for us had to do with the fuse box. There was a couple of pieces broken off (over time) that wouldnt give the right connection to the battery. There should be a cable or two (tubes) connected from battery to fuse box. We would always move it around and it would start again. Other than that i don't know man. Maybe your alternator?