I believe I have fixed the problem - I had this very very frustrating issue!!!! You get into the cockpit think you've got the start up procedure to a T and then when you move your left throttle fwd it doesn't kick start the turbine, right?
Ok well here's the fix: (make sure you save .lua fule in a separate loc if you do not want it perm overwritten - all will become clear!!!)
1. Go into A10C and then OPTIONS and then CONTROLS (on the single player not multiplayer). If using TM Warthog (or whichever rig you have) then click in one of the config columns (with the GAME tab selected - so basically you're updating the controls for game not simulation mode.
2. Then click on LOAD PROFILE and copy the .lua profile for your rig from the A10C folder. NB when you click LOAD PROFILE it will default to the A10C Easy folder you need to find the sim mode sub-folder.
3. Do this for both THROTTLE AND STICK and finally click on MISC and uncheck 'synch TM Warthog at mission start' or something to that effect.
Do not ask me why this works - after racking my brains out for nearly four hours and pain stakingly trying and testing combinations I go this to work!!!!