Hi. I would look at the fuel panel at the Flight Engineer's station first. Is this when you do your own start? Does it happen loading the default L1011 Cleared for Takeoff file? Here's how that's set up:
It will work in other configurations, too, as long as you're getting fuel to your engines. I seem to remember having to learn this the hard way when I first started with the L1011.
As for the autopilot, you have to get used to the different pitch modes and what they're for and realize you are ALWAYS controlling your throttles except when on autoland (or, using the autothrottle switch, which I reserve for cruise, and recommend avoiding it until then to get used to the airplane and learning the different pitch modes, but that's just my opinion).
If you get set up climbing at 250 kts at a certain throttle setting, then hit the IAS button, the autopilot will do its best to maintain that climb, but only by pitch. Vertical speed will try to maintain whatever you dialed in, but you must have the throttles pushed forward enough to maintain it.
If you're relying on the automation for knowledgeable flying, it serves well. But if you expect it to fly the TriStar for you, it will kill you, especially during climbout. It doesn't have any built-in protections and will happily stall you and kill you if you've messed something up.
The reason I'm going into this detail is because the autopilot works much differently than we're used to from other airplanes. In fact, I spent a few days doing nothing but taking off and experimenting with the pitch modes so I learned what each one does and which is better for what I want at a particular time.
And don't worry about joining the "I Stalled the TriStar" club. I stalled plenty of times, and once you start, you are never going to pull out no matter what you do. It is a very unforgiving airplane. Another good learning method is just to take off and fly around without any automation at all in violation of all aviation rules and regulations. I call that "fly it like you stole it."
Hope some of this helps and keep at it.
Tim