lets break this down a little bit:
He has a SK Sin:Ok, so he has a SIN, this means that his prints and biometrics are on file with the SIN database and any biological evidence (hair, fingerprint, blood, saliva) left at a crime scene can be used to link him to the crime. Once that link is established, his SIN can be used to track is movements through the city/country/world. The fact that it is a SK SIN makes no difference to the local legal authorities. And it offers no special protections to the holder of the SIN. If he commits a crime off SK property and is arrested, there is nothing SK can do about it, If he lives on SK property and commits a crime outside of side property, all the SIN and living address means is that the Authorities have to ask SK to arrest him and turn him over. MOST Megacorps will do this for the average "Joe Worker" because it more helpful to be on good relations with a country/city then it is worth protecting a peon in the system. Even if SK doesn't agree to turn him over, he is fair game once he steps foot off SK Property.
He refuses to Kill Good for him!! Shadowrunners don't NEED to kill to pull off the average run... it's just usually easier then taking all the Precautions of Not killing. In fact, the only job that requires a Runner to kill is a wetwork job.... And Runners who do them or go around blasting people on a daily basis USUALLY don't have a long career. (the law looks A LOT harder for the guys involved in the murder of 15 people then they do looking for the guys that stole a "widget") Seeing as how most players play shadowrunners as barely functional psychopathic serial killers, someone who plays a character with Morals should be rewarded for the effort.
He will only take runs related to his brotherTo quote a great TV show: "I don't think so Tim"
Sorry, but that's just not the way it works. In this case HE is the one that wants info on his brother. So what is he doing to find him? Has he hired a private investigator? Has he been back tracking on his brother's last know activities, friends, and location to see if something stands out in his disappearance? Has he been doing ANYTHING other then sitting in his apartment waiting for the info to fall into his lap?

All that costs money you know. A single private investigator costs between $200 - $500 PER DAY! ($1000 to $2500 per WEEK, $4000 to $10,000 PER MONTH!!!). So how is he paying for all this searching? Does he have the skills and contacts to do it himself? (I am guessing not as it is a specialized skill set and not many people put the effort into getting all the skills needed to be able to track down missing persons)
In short, he is acting like a Johnson, HE wants the info/widget (his brother), now he has to hire someone to track him down. But since he has no job, how is he going to pay for tracking down his brother?? (Enter... SHADOWRUNS!!!)
Doesn't fit in with the rest of the teamHate to say it, but this is kind of the FIRST rule of any roleplaying game. If a character doesn't fit in with a group, Why is the group hanging with this dead weight? It's not like they are physically attached to him by a surgery or handcuffs. Just as in real life, when someone is dead weight, they get cut loose. Same with a shadowrun team. If this character doesn't "get with the program" then its time for the team to find someone who will (and lets face it, there is lots of talent in the barrens areas of cities that would jump at the chance to make the cash that a shadowrunner makes...)
Does this mean you/they are ditching the PLAYER? No, he has just basically made a character that is more suited to a solo game and not a team based character. So either they (the other characters) sit him down and tell him to "get with the program" or they cut him loose and hire a replacement (his "new" character), or they pool their resources and "solve" this brothers disappearance (and probably go broke doing so)