Callum,

Try this. Load up your aircraft at an airport. I am guessing the state maybe a mix of fuel on, engines off, instruments dark. Start the APU. Do this first. Hold the APU button until you see the needle in the gauge begun to rise. Release the start button. Once you see the APU lights in the panel above start it.
To save all pain I recommend you now set up the cockpit state as you want. I have a APU running type set up. Once you are happy with your choices, go to the menu in FMC, options and Panel State then Custom Panel and save and name your current state. Good to go!!

When you restart the sim again, I have found you will need to start the APU again as above but then simply go to your saved custom panel and load it. It’s a little fiddly but works fine for me.

PM me if you need any more help and I can give you an email. Whilst the classic has a number of bugs, it’s worth pursuing. Good luck.

Keith.