The day before car started and run just fine, no sign of any problem what so ever. Next morning I started the car, engine was shaky like in case when one cylinder doesn't work, so I turned it off.
On the next attempt the same symptom occurred and suddenly the engine died out. I took a walk to work and though that I will troubleshoot later with VAG-COM to find out the cylinder and replace the ignition coil (just had the case 07/2013).

Next attempt in the evening was a bit scary as when I tried to start the car it wasn't making a normal cranking sound, but strange constant weeeeee.
Serpentine belt moves, as much I was able to see I didn't notice any signs of engine belt breaking, troubleshooted with VAG-COM without any success - no codes. Hours of google and forum searches without any match point result.
...spent some additional hours on research and is this the worst nightmare that timing belt slipped, bent the valves and this constant weeeee sound on cranking the engine is signal of no compression?

 

In summary what I have verified:
1. Serpentine belt moves
2. Engine aka timing belt moves ( I haven't verified timing as car is not in the place where I could removed belt cover, which means bumper removal)
3. Intake and exhaust cams are moving
4. Measured compression in cylinders, about 30 psi
(of course ign. coils ar ok, spars are ok, fuel pump is ok, fuel pressure is there)

I haven't yet tried to put a tablespoon of oil through spark plug holes. Do you recommend doing it or is it already obvious that I need to take the cylinder head off and inspect the valves?
What are the reasons to lose compression other than bent valves

What I noticed with valve cover open is that cam chain tensioner isn’t going up. I have understood that it should move up and down?

Back to the beginning where I stated that I wasn't able to get any fault codes with Vag Com nor the engine light came on. So when I removed everything necessary to get the valve cover open, then all disconnected connectors (also fuel pump fuse nr. 28) triggered fault codes, but then again these were triggered by me:
10 Faults Found:
17645 - Fuel Injector for Cylinder 1 (N30): Open Circuit
P1237 - 004 - No Signal/Communication
17647 - Fuel Injector for Cylinder 3 (N32): Open Circuit
P1239 - 004 - No Signal/Communication
17648 - Fuel Injector for Cylinder 4 (N33): Open Circuit
P1240 - 004 - No Signal/Communication
17646 - Fuel Injector for Cylinder 2 (N31): Open Circuit
P1238 - 004 - No Signal/Communication
17833 - EVAP Purge Valve (N80): Short to Ground
P1425 - 002 - Lower Limit Exceeded - Intermittent
17525 - Oxygen (Lambda) Sensor Heating Circuit: B1 S2: Short to Ground
P1117 - 002 - Lower Limit Exceeded - Intermittent
17843 - Secondary Air Pump Relay (J299): Short to Ground
P1435 - 002 - Lower Limit Exceeded - Intermittent
17829 - Secondary Air Injection Solenoid Valve (N112): Short to Ground
P1421 - 002 - Lower Limit Exceeded - Intermittent
17697 - Boost Pressure Control Valve (N249): Short to Ground
P1289 - 002 - Lower Limit Exceeded - Intermittent
17949 - Fuel Pump Relay (J17): Open Circuit
P1541 - 004 - No Signal/Communication - Intermittent

 

Reason for this problem was stuck piston rings at all 4 valves at the same time.
Root cause is unknown.