This could be many things. I don't have the impression this is due by a lack of gas though. A bad knock sensor (or not connected) for instance would automatically put the engine in safe mode and reduce the timing, but it can be many other things and your best bet would go to a place like Autozone where you could have a free diagnose. Otherwise it's almost impossible to know.
Good luck !
Fuel injection systems of 10-15 years ago (and older) used to have grave warnings in the manual about never letting the car run out of gas, and if you did, to take the car to a dealer for a purge of the system. The problem, as I recall, was bubbles in lines potentially blocking flow. Don't know if this is still an issue, but I don't see the same warnings in my book (I've got a 2003 VVT-i V-6 myself). You'd think on a modern car, any problem would trigger the CEL. I assume you don't have the light. Might still be worth a consult at the dealer service dept. Alas, I doubt such self-inflicted damage is going to be covered under the wty. . . I don't have much right to point fingers, since a couple weeks ago I pumped 18.3 gal into my 18.5 gal tank, but what were you doing the whole time the low fuel light was shining in your face??? Oh yeah, per the manual, you're supposed to get a CEL when the tank runs dry, while there's still gas in the lines. Manual advises getting gas right away (gee, good idea). Did you see a CEL before you ran dry, and if so, how long did the gas in the lines last?
My hunch is your fuel pump got hurt. In-tank fuel pumps needs lotsa gas for lubrication and cooling. If you let it run dry, it will get damaged. It's good practice to gas up once you hit 1/2 tank, or 1/4 tank at the very most.