I would say a critical thing would be the ability to validate the answer.
So - I'd think of the following things, can I somehow attribute the original question or make it my own?
If deleted for quality or content, and your answer is substantially or completely your own and has good quality and content, go for it!
If you have the same problem, and are able to write your own question, and test the validate the answer, there's no reason you can't.
If there are other issues in play - and there's nothing actually wrong with the question...
Would undeletion via flag be viable? - in which case one could fix the original question, and rely on voting to float up the correct answer. If the question is perfectly good, but deleted because of other reasons, it might get messier. I'd suggest asking on local meta for advice if you have a link. Otherwise, just go for your own question.
If the person asking the question is active, and the question was roombaed, undeletion would definitely be the answer
So largely - yes, go ahead and ask your own question on the problem and no one ought to particularly mind.