I assume nothing happened to the engine, there is a RPM limiter as a safety, cuts off the fuel.
Looks like your bowden cable is stuck. Here is the part number, recheck the p/n with your VIN http://de.bmwfans.info/parts-catalog..._bowden_cable/
Gaskabelzug 35411162171 abt. 15 EURO.
There are BMW Throttle safety clips, scroll down here http://www.nmia.com/~dgnrg/for_sale.htm p/n 35401165393 Prevents throttle cables from detaching, which can cause dangerous unintended acceleration
make one DIY http://i106.photobucket.com/albums/m...L/DSC00075.jpg

The plastic screw is basically the problem, here a cheap fix , Throttle Bushing repair for $1.72 https://www.bimmerforums.com/forum/s...epair-for-1-72