With my 13 year old dd, until recently similar tensions over homework and similar computer ban. But actually, my dd hadn't been getting in trouble at school (that I know of), it's just that she did it last minute/late etc or asked us for ingredients for food tech at midnight the night before etc.
Eventually, we discussed - I don't want to be wasting my time monitoring her homework and don't care if it's all 'perfect' as long as it's done on time. She wants not to be nagged and to have computer access. So we agreed I'd give her a month to organise herself, give us good notice of ingedients/anything else she needed, and if by the end of the month it was going fine then we'd leave her to get on with it, if not we'd go back to my checking her homework and insisting she did it as soon as she came back from school. It's now over a month and she has been doing it - not as soon as she comes in, which I'd prefer, usually in front of the TV which I don't really like, but doing it. And we've stopped rowing about it.
Could that approach work for you? - explain that you want to treat her as an adult provided she behaves like an adult - if not, then she'll have to go back to being treated as a child until she's understood how important it is to stay on top of school work, even if she finds it boring.
If she's actually getting in trouble at school or v behind then this approach might not work, I suppose - in that case she might need your help to actually do the homework. She might be resisting because she just can't actually do it but is scared to admit this - know my dd was like this before exams last summer. I discovered the reason she wasn't revising for her exams was because her notes were rubbish (gappy/illegible) - bought her some Letts Revise KS3 type books and she got down to revising quite happily (and did v well in the exams). Don't be angry if she is behind - will only make her feel worse - just make it clear you're happy to help or advise or get extra resources etc if she needs it and otherwise you expect and trust her to keep on top of it herself.
You can use the computer time positively rather than negatively eg as a reward for effort put in not removed as a punishment for 'naughtiness'.