Does The 10-year/100,000 Warranty Apply To Engine Problems?

The car: 2001 Hyundai Elantra purchased from a dealership with the then-exciting 10-year/100,000 warranty attached. Over the years, it hasn't covered anything -- from burnt-out headlights to power steering -- the warranty's never "covered" any of my car troubles. They told me it covers stuff under the hood so now, with my engine problems, I should hypothetically be covered, right?

The problem: The engine. The Check Engine light had been on, but the car drove fine. At least once every drive, the engine would kick up to 3 or 4 RPMs and change sounds (I'd describe the sound as if the engine was constantly "revving up") and then eventually go back to normal. Now just last week, the engine began sputtering -- still drivable -- but making a loud, constant sputtering noise. In addition, it stalls at red lights/stop signs.

So what can I do? Will the warranty finally help me in this case? I'm just a college student who needs a car to get from school and work and back again. Something tells me it's going to cost a lot of $$$ to fix and I'm just looking to get the best deal available. Thanks.