Need to know why my 2003 Hyundai elantra is suddenly shutting completely off while driving

Hmm not sure...Had a similar issue w/ my '02 Elantra. Check Engine light had been on for a while, was told it had to do w/ oxygen sensors. Most recently the car would stall, idle at very low RPMs, and did not have much power and would sputter through turns. End result was only a clogged fuel valve, and that seems to have done the trick. A lot of these issues posted regarding older Hyundai Elantras seem to all relate back to the fuel source...good luck...

If you have already replaced the fuel pump, I would suggest removing and cleaning the throttle control body. This is a known issue in older models of the Elantra, but is a simple fix. It shouldn't take more than 30 minutes, start to finish. Just use a clean cloth, rinse often, and MAKE SURE that the throttle control body is completely clean AND dry before reassembly.