How do you start a jet engine if the start valve is stuck closed?
Perusing the A380 Training Guide, Edition 01, 01 Sep 2008, Section 5 - Engine Starts, Subsections 5.8.6 (Engine Start Valve Stuck Closed),


  5.8.6 Engine Start Valve Stuck Closed
  
  
  ECAM actions – ENGINE MASTER OFF.
  Check MEL, and in conjunction with, advise LAE of situation in preparation for Start Valve Manual Operation.
  For Start Valve Manual Operation on Engines #2 and #4, the adjacent engine (if already running) will require shutdown, to enable LAE’s
  access to the manual start override procedure on the port side of the
  affected engine.
  As the CAB Pb on the RMP is common to the Cockpit, Ground and Cabin Crew, advise the Cabin Crew to refrain from using the Cabin Interphone
  during the procedure.
  When ready, accomplish normal engine start sequence:
  a)    Engine Start Selector to IGN/START.
  b)    Engine Master Lever to ON.
  c)    Command LAE to OPEN START VALVE AND KEEP OPEN.
  d)    At 50%N3, command LAE, START VALVE CLOSE.
  e)    Monitor engine parameters closely until stabilized.  
  Advise Cabin Crew upon completion of procedure.  
  In flight, only windmilling start will be available.  
  


Glossary (correct if needed, please):
ECAM = Electronic Centralised Aircraft Monitor
LAE = Licensed Aircraft Engineer
CAB = Cabin
Pb = Pushbutton
RMP = Radio Management Panel
IGN = Ignition
N1/N2/N3 = N1 is LP (Low Pressure stage), N2 is IP (Intermediate Pressure stage), N3 is HP (High Pressure stage)
MEL = Minimum Equipment List


ECAM will display "ENG MASTER X ........ OFF" (X will be the engine with stuck valve)
(A320 display, only shows two engines, instead of four) (The message will appear in the lower left quadrant.)
Check the Minimum Equipment List (MEL) to determine if loss of engine is GO, GO IF, or NO GO, if failure is not in the MEL, it is classified by default as NO GO. Advise the on-site Licensed Aircraft Engineer (LAE) of the warning message in preparation for completing the Start Valve Manual Operation procedure.
If the engine with the stuck valve is #2 (left side inboard) or #4 (right side outboard), the adjacent engine will be required to be shutdown before commencing the manual start procedure. (This is because the engineer has to access the left side of the engine and for safety's sake the other engine, which would be gehind him must be shut down. If the fault is on the left outboard (#1) then the engineer would be on the far side of the engine from the #2 so #2 does not need to be shutdown.)
Since the Cabin Pushbutton (CAB Pb) on the Radio Management Panel (RMP) is common to the Cockpit, the Cabin Crew area AND the Ground circuit, the pilot should advise the Cabin Crew to not use the Cabin Interphone during the procedure. (If the pilot and the engineer are discussing starting the engine (or not) they don't want a flight attendant to be talking about starting pre-flight stuff at the same time, if the engineer heard the word start, he might wrongly assume it was the pilot.)
When pilot and engineer are ready, begin the normal engine start sequence with changes:

a) Turn the Engine Start Selector to IGN/START. (This is a panel from an A320, so only two engines are shown.)

b) Flip the Engine Master Lever (For the faulted engine) to ON. (This is a panel from an A320, so only two engines are shown.)

c) Over the interphone, command the engineer to manually open the start valve and keep it open. (I haven't yet looked for and found a schematic for an example engine, sorry. As shown in other diagrams/answers, it might be a socket wrench, etc.)

d) Watch the Engine Warning Display. (Again, A320, only two engines.) (This is an A380, showing N3) Once N3 is spun up to 50%, over the interphone, command the engineer to manually close the start valve.

e) Monitor the engine parameters closely until all are properly stable.

f) After the engineer has closed up the engine and vacated the area, start the other engines, if one was shut down per step 3.
Over the cabin interphone, notify the cabin crew that the procedure is complete. ( so they can resume using the interphone if needed. )
If the engine failed in-flight and upon restart a stuck valve warning was shown, all of the above would not be possible. At that time, the only way to restart the engine would be to attempt a windmill start (using the flow of air through the engine to turn the engine), there are other procedures for that.


Also, I do not yet have the engine schematics to show what the LAE actually does.