Is there a risk of starting the laptop?

I'm currently troubleshooting and have to test whether the fan is rotating,

Is there a risk of cleaning the battery and testing it?

As long as you keep your fingers off and haven't changed anything, there shouldn't be any risk…

Why do you have to test whether the fan is spinning?

Yes, there's always a risk with something like that. For example, Fall a screwdriver on the motherboard and cause a short circuit.

In short: I would let it be

So if you have to ask a question like that, I don't know if that's a good idea, whatever you do.

Now screw your laptop back on and see that nothing breaks.

You can hear and feel whether the fan is rotating.