Please note: these are not ALL the possible reasons for someone having difficulty getting started, and any assumptions based on the following could turn out to be incorrect for the individual student you're dealing with. It is absolutely vital that we parents and teachers be respectful enough to ask them. You never know, that one simple question might save months or even years of angst.
Fear of failure - We all hate feeling like a failure. Young people/adults/children refuse to partake of activities often because they are afraid to be laughed at, or even simply afraid of finding out they aren't very good at something.
Fear of success - my son once told me that he didn't want to excel at school, because that would set up an expectation of success level from the adults at school - an expectation he didn't feel he could consistently work to. Sometimes people are also afraid of success because they don't have a concept of what that successful experience could look/feel like. The unknown terrifies them and thus holds them back.
It's all too much Type 1 - the student could be in overwhelm for any number of reasons. Try to learn what this looks like and be alert to when it might be happening. Work out a management strategy with your student, such as giving them a ten minute break from the noisy classroom so that they can re-group. Wherever possible, try to incorporate strategies like this as preventative steps rather than reactive solutions. This gives the child some control over their own behaviour management as well.
It's all too much Type 2 - sometimes the task is just too complicated or detailed for your student. Or there could be too many steps involved. Quite often students on the spectrum will have fine motor delay, which will mean they are slower to get work done. If the task seems too big or time-consuming, they will avoid it. In this case it's a good idea to cut the task down into smaller chunks (you teachers know that word "chunking"!), and give your Aspie student a reduced list of steps to achieve. How much you cut this down will depend on your student, but a good rule of thumb is to take the chunking you think is age appropriate and double the number of chunks (i.e.: create smaller bites to chew). You might even need to give them one small step at a time, as the awareness of the second step could be enough of a distraction to prevent commencement. NB: I have had a teacher say that they don't like this idea, as it felt like he was treating the student as someone much younger, and he didn't think that was okay. But please remember, it's never condescending to give your student what they need in order to learn. You're doing them a favour by adapting to their needs instead of forcing them into your worldview, and they don't know (or care) what level of chunking is age-appropriate, so it's really (honestly) a good thing for you to do it. Very small chunks could mean that your student finally experiences success. Isn't it exciting to think you could be the catalyst for that experience?
It's all too much Type 3 - Your student might have poor executive functioning (ability to plan and organise their work/thoughts/body). Around age 7, my son found this so difficult that when he was asked to sit and write something, he would sit with a piece of paper in front of him, behaving perfectly, but he would write nothing. As it turned out, the reason he had not begun was because it had not occurred to him to bring a pencil to the table, and he couldn't figure out what was missing when it came time to get started. This is a very intelligent child who simply could not work out what to do, because he couldn't think that many steps ahead. So you might find that with your student, you will have to do a lot of organising for them. Your objective is to build independence though, so try to give them systems to follow, rather than hand-holding through every step (although you will have to be diligent and patient as they build the neural pathways to be able to do this for themselves). A simple idea might be to have checklists stuck to their desk (such as 'What equipment do I need?'), so that they can work through a list of what to do next for fundamental tasks like preparing to write. But remember to be patient. It will take a long time and a lot of support for this skill to find its place.
Didn't catch all the instructions - a student with attention difficulties (this is also a common side effect of sensory overwhelm), might only hear part of the instructions. This student will frequently be unwilling to ask you to tell them again, because they have often found themselves being disciplined for not listening properly. Often instructions called out from the front of the classroom don't work for the student with Autism, because all that student hears is "yelling". After instructing your class, approach this student and (rather than repeating everything you just said), ask her to tell you in her own words what she needs to get done. This will give you some awareness of what she has understood, and an opportunity to clear up any miscommunications. It is also helpful to list instructions on the board as a ready reference, as your student might not be able to retain more than one step at a time.
Perfectionism - we see perfectionism in young children all the time, and it's a tough one to break, but it's vital that we do, because the anxiety related to this can completely prevent commencement and cause much bigger problems down the track. This is fear of failure at its worst. I recommend having a Mistakes Are Good Because We Learn From Them whole classroom culture. Also, many teachers make kids earn a pen licence (they must be able to write to a certain quality before they are allowed to use a pen for their classwork). I recommend doing the complete opposite, because kids can't erase pen mistakes, so they can get used to seeing that they aren't the only ones who have errors in their work. Another positive side-effect is that teachers can see what errors individual students are making, discover gaps in learning and plan future classes accordingly. Also, the child with fine-motor delay is rarely if ever going to meet the standard and thus earn the pen licence. Do you really want them to feel so bad by pointing out that they can never, ever measure up to their peers?
Sensory reasons - sometimes you will have a student on the spectrum who will refuse to start an activity or join in, but there doesn't appear to be any rational reason for this decision, and they aren't telling you what's wrong. Look for reasons such as those outlined above, but also be sure to ask a clear question such as, "Is there something specific about this activity which is preventing you from joining in?" My son has an irrational fear of styrofoam (related to the squeaky noise it makes). As articulate and verbal as he is, when faced with the prospect of an activity involving styrofoam, he will completely shut down and refuse to even enter the room, quickly losing the capacity to explain what is wrong, without adult intervention and assistance. If the issue is a fear like this, there is no reason worth forcing them to face the fear in front of their peers. Let it go, find another activity for this student, or change what you are doing in the classroom so as to include them.
And don't forget - it's imperative that we ask the direct questions, or we'll never really be sure we have the correct answers.