Whatever he aspired to achieve, they were hindered by his jealous step brothers.

Dangling participles are not used here properly. Participles of verbs are often used to introduce subordinate clauses, which give extra information about the main part of a sentence (known as the main clause). It’s important to use participles in subordinate clauses correctly. The participle should always describe an action performed by the subject of the main part of the sentence. For example: Travelling to Finland, I found that the weather got colder and colder.So, All the main clauses starting with ‘they’ are incorrect. Go for details: https://www.lexico.com/grammar/dangling-participles