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You're going to have to use a civil rights lawyer but the problem is that the court system is exempt from a lawsuit for actions taken in their official capacity, as is the DA. The police aren't necessarily immune so almost certainly the lawyer will end up trying to make the case against them.
However, it is unlikely the civil lawyer is going to start on the case until the criminal case is resolved. Possible, but unlikely.
The only real thing you can do to start is to locate a lawyer practicing civil rights law. You can find one at www.lawyers.com and in the Area of Practice box enter "civil rights law".
You will also need to get a power of attorney (POA) from your brother to be able to hire the lawyer and sign the contract on his behalf but there's no need to do that until you locate a lawyer who is interested in the case and they can probably provide the POA for you to get him to sign.
It has to be done through the criminal process. If the case is in the Texas court of Criminal appeals then you have to wait until they rule. No other court has jurisdiction to overrule them or force them to rule on a matter or at least not for a long time. At some point, there is no specific time, a case could be filed in the federal court system saying that the TCCA's failure to rule is, in effect, a denial of the right to be released (probably through a writ of habeas corpus) but my suspicion as to time is that it would take a year or more without a ruling and anything before that would be dismissed.
In addition, that's not going to be a civil remedy, that has to be done through the criminal system and you'll have to hire a private lawyer to do that. No one will take that part of the case on a % basis.