Learn Hardcore Japanese: pasokon ga ugokanai to, syukudai ga dekimasen. - If the computer doesn’t work, I can’t do my homework.

It marks the grammatical subject. 動く/動かない is an intransitive verb (“to move/work by itself”), so you can’t use を (which marks a direct object). パソコンが動かない literally means “the computer doesn’t work,” with パソコン as the subject.

Why is 動かない in plain form instead of the polite 動きません when the main clause is polite?

The conditional particle と attaches to the plain form. In Japanese, subordinate clauses (like conditionals with と, たら, etc.) are usually in plain form, even within a polite overall sentence. Hence 動かない + と + できません.

What role does と play in 動かないと、宿題ができません?

Here と is the “if/when” conditional that expresses a natural or inevitable result. It means “if/when the computer doesn’t work, then I can’t do my homework.”

Why is it できません instead of しません when talking about homework?

できる/できません is the potential verb meaning “can do/cannot do.” しません would just mean “don’t do.” So 宿題ができません means “I can’t do (or cannot complete) my homework,” not “I don’t do my homework.”

Why does 宿題 take the particle が in 宿題ができません rather than を?

Potential verbs like できる/できません use が to mark the thing that can (or cannot) be done. Contrast: 宿題をする (“do homework”) vs. 宿題ができる (“be able to do/finish homework”).

Can you replace と with たら or ば in this sentence?

Yes.
– パソコンが動かなかったら、宿題ができません
– パソコンが動かなければ、宿題ができません
The nuance changes slightly: と suggests a straightforward, inevitable result, while たら/ば are more hypothetical or conditional.

Could you use は instead of が in パソコンが動かないと?

You could say パソコンは動かないと, but it shifts the nuance. が highlights the condition itself (“the fact that the PC won’t work”). は turns パソコン into the topic and can imply contrast (“As for my PC…”).

How would you say the positive opposite, “If the computer works, I can do my homework”?

Change to the affirmative forms:
パソコンが動くと、宿題ができます。
Or with たら/ば:
パソコンが動いたら／動けば、宿題ができます。