Sounds like there's a few things going on, and the comments are all over the place. They're all good though! :) Here's what you need to do.
1 - Check engine light is on: The computer is trying to tell you what's wrong. Get the code read by the shop and post back here.
2 - Car quietly not starting: As has been suggested by others, this is most likely the "neutral-start inhibitor," a tiny little switch that will prevent your car from starting in other positions than "Park" or "Neutral." Your car may very well be in "Park," but if the switch can't see that, it wll not let your starter do it's thing. Three things you can do to diagnose this and work around it. If any of the following 3 techniques get the car to start, the issue is the switch:
- apply the hand-brake, turn your key to "on" without starting, press the brake pedal and shift to "neutral," now try to start the car
- if that didn't work, try hand-brake, key to "on" without starting, press the brake pedal and now shift all the way down to "L" then back to "Park", at least twice. When you're back in "Park" for the second or third time, try to start the car
- if that didn't work, your last try is to find the "sweetspot" in "Park." My '94 Nissan had this issue (still does), where the shifter would be in "Park", but it could move around a little bit while still staying in "Park." When in "Park," gently push the shifter as far forward (towards your heater controls) as you can and hold it there while trying to start. If that doesn't work, try gently pulling it as far back (towards "reverse") and hold it there while trying to start.
3 - Car lurching and lunging in low gear: if this is new, you may have a transmission problem (your torque converter may be locking-up when it shouldn't). If you've just used low-gear for the first time and noticed this, it may be normal as some cars are really jerky in low-gear.
4 - Grinding belt noise: you may have a pulley that seized, preventing the belt from circulating properly. If that's the case, most starters are not powerful enough to turn your engine over (that noise that it's supposed to make when trying to start) if a belt is seized. Have your belts removed to see if the car can start easily now.