Attack of the Cosmic Rays!
I think you should start with the Attack of the Cosmic Rays! - a single high energy particle (coming from space and reaching computer here on Earth) can flip bits in computer memory, causing all sort of errors.
However, I would expect your spaceship to have proper shielding against radiation. Including everything that could be harmful for the crew, in particular when their ship is outside the natural protection of a planet. That means that high energy photons, electrons, protons, alpha particles even muons would be covered.
Addendum: About the ionized nebula gas. It is to be expected. If the ship is particulary vulnerable to it, I would blame it on human error: bad ship design.
I would not expect to have dedicated shielding against neutrinos. That would be very inefficient. Instead, there are technologies for error detection and correction that can deal with single bit flips.
Let us say, all that failed (which is very unlikely, but there are many neutrinos, and I am underselling it). The problem is usually in working memory, then the solution is simply to reboot the system.
You could work in reasons why they cannot reboot the system, for example the computer could be working in something mission critical and we do not want to lose progress.
Alternatively, you could work in reasons why a reboot does not work, for example the problem has already been committed to persistent memory. They try a reboot and it does not work. And restoring a backup would mean losing too much.
Or you could work in reasons why persistent memory was what was compromised. In which case, the problem is detected after a reboot. This could make it seem like human error.
On high energy events
If something so drastic happens that can affect her emotion core, it can affect any electronics on the ship. Either the ship has proper shielding, and then nothing special happens. Or the ship is better of avoiding the event or going dark while it happens.
I am aware that a high energy event could dramatic, which is useful for storytelling. On the other hand, without a high energy event... you can have the crew slowly figure out that something is wrong... for when they notice, it would have happened an unknown time in the past, and they would not know the spread of the compromise.
However, you can split he event in two: the first is an accident that results in her shielding being compromised (that part could be human error, or not), the other is external high energy event. For example: a micro meteoroid hits the ship while traveling at relativistic speed compromising the shields, then radiation can enter, such as the ionized nebula gas.
Even if the problem can explained only by the high energy event, I would consider it a mistake to be where it would happen. If there is any way to predict it, a fly path away from it should have been found.
Thus, we need something really hard to predict (we know Coronal mass ejection happen in periods of high stellar activity, and there are signs that a star is near the point it will go Supernova, so we can avoid those)... in that case, I want to suggest Gamma-ray bursts.
Ah, all of that is without considering her an AI. Let alone an AI with emotions.
Being the damage on the emotion core only helps to divert the attempts of the hacker to discover what is up.
It is a convergent goal of AI to survive (so it can perform whatever task it has as goal), and thus, AI does not want to be shut down. She will resist and fight against any attempts to reboot her.
Addendum: Futhermore, the AI could decide to destroy the backups to prevent the hacker from attempting to restore them.
Considering the emotion core damaged, every emotion she displays could be justified to some degree... For instance when the hacker is trying to fix her: She could be happy that they are doing it, sad that they have to do it, ashamed that they get to see her like that, guilty because of the trouble she caused, disgusted with humans messing with her internals, angry that they are trying to alter her, afraid of what will be her, surprised by the skills of the hacker... heck, she might even behave as sexually aroused. I suppose it is best to write her as inconsistent.