Your specific situation seems to be actually quite simple: D8.1 says
An immobilized vehicle cannot expend a Start MP, leave its current Location nor change its VCA, but may otherwise change its TCA if otherwise able to do so.
What does otherwise able to do so mean, you ask? Well; if, your suspicions aroused by the word also in your own quotation, you check the rest of the paragraph, you will find that "...whenever a vehicle fires a turret-mounted weapon outside its VCA...a turret counter is placed." with no mention of Immobilization. So, despite what you might think, the tank does not change its TCA and then fire: it fires at whatever target it wishes, and then places or moves the turret counter.
More generally: though an immobile vehicle cannot do the things mentioned above (i.e. move), it is still covered by B2.1 " a vehicle may expend up to its full MP allotment during its own MPh". So there is no reason it cannot fire smoke dispensers. load/unload passengers, and spend Delay MPs if it wants to Bounding First Fire.
For reality check purposes, consider that even if the turret rotation works off the engine (some had batteries, and most had hand cranks for emergency), a combat Immobilization result is likely to reflect a broken track or wheel rather than complete loss of power: the crew have already passed an Immobilization TC, so they think it possible to stay and use the weapons.
Later: Though this answer is correct, I forgot that in ASL it's not the actual rules you have to worry about, but the exceptions to the exceptions (and the ambiguous phrasing). C5.2 says "A Bounding First Firer must always fire within its current CA: it may change that CA only via MP expenditure." So since the tank did not change its CA as part of the start procedure, it must now spend another Delay MP (or possibly three, to avoid the Limited Aim penalty (cue the argument about whether you had LOS to the gun at the start of the phase, when you saw the hex, but the gun was still Hidden; cf. C5.33, which clearly supports both possibilities)) which accomplishes nothing, but allows it, free as part of the MP expenditure, to change CA and thus fire. As a limited consolation, the same paragraph says "[The penalty for changing CA] is never applicable to an Attacker firing during his own MPh."