heck your fuses first, if the one for the fuel pump is not bad (but check them all just in case), then when you turn your key to the ON position without turning it over do you hear the fuel pump kick on? it sounds like a small electric motor. you will have to listen carefully to hear it. it should stop humming after about 3 seconds. if you do not hear the pump kick on and off then you need a fuel pump. that is what i bet it is. but if you do hear the pump working, then you have a problem with the cars internal computer...which sucks. so you should hope its just the fuel pump. good luck!

Pop the oil cap off, crank it and see if the cam/lifters are moving.

Could just be a blown timing belt.

It sounds like what happens to an engine when it looses oil pressure, the bearings actually speed up and then seize up. There is more behind this story that you haven't disclosed, the RPM's didn't just shoot up while driving unless the clutch was slipping or the driver accidentally downshifted and floated the engine valves. You likely have a toasted valve train if the RPM's went over the red line.

Does the motor spin faster than usual and not shake when trying to start it?

Is that a turbo diesel car ? If its it can be what we call a runaway, if it happend you wpild have noticed a cloud of grayish smoke

Does the motor spin faster than usual and not shake when trying to start it? If so then the timing belt has broken. This a non interference motor so the valves will be ok. Tow it to a shop or home. 2 bolts on valve cover to confirm. Remove and watch the valves go up and down on starting. No movement and t-belt gone.

I was driving on the freeway and out of nowhere my rpms shot up an went back down. It stayed running for like 30 seconds after that. When I pushed the gas nothing happened. Then it just shut off. I tried starting it after that, and it wouldn't start. It turns over but it doesn't start. I have an 88 Honda accord, does anyone know what this could be?