My engine died and won't turn on 2001 Golf

if your batery is dead. it's the alternator. If it just plain died and everything else works I'd take it back.

you turned up the fan speed , correct? While that electric motor doesn't draw alot of current, it could be coincidental that everything died. But have the charging system checked....sounds to me like the battery died completely or you have a short in the controls to the fan. Easiest thing to do is either first get a jump start or swap the battery. If car runs like normal, battery is suspect and should be checked along with your charging system. Timing belt would not be an issue here because you would not have been able to drive the car.....after starting it would have died immediately.

if the engine fails to rotate, the problem may range from a worn strter to broken engine component.
in your case, this happened while you were driving....

- Attempt to rotate the engine by hand. use a socket and ratchet on the cranksaft pulley nut and attempt to rotate the engine trhough two complete revolutions.
if the engine cannot be rotated through the two revolutions,the engine may have internal parts breakage.the broken components may have lodge into the cylinder block preventing the engine from rotating.
in addition ,engines with interference fit combustion chambers may have valves imbedded into the tops of the piston if the timing chain (or belt) slips or break. To verify this, remove the valve cover a ? or the oil pan and perform a visual inspection.

So it's your alternator or they screwed up on your belt.....again...really not that bad. It's either a 60 dollar alternator or a free engine.