But that's 60 points, and you can only get 35 points worth of negative qualities! Typical munchkin, cheating already.

Okay, all kinds of ways to make a character useless, but here's one. Start out as a full mage, with Magic of 6, then get 4 cyberlimbs and a cybertorso, with enough of it alphaware that you have 1 point of magic left (but no cyberlimb mods at all!). Take the Sorcerer negative quality to make all of your non-spellcasting skills nearly useless - get them high enough that he can roll one or two dice for them, but get spellcasting lower, along with a few spells that are useless at low force. Avoid counterspelling, which could actually be useful for this character. Mental stats will be high, so mess up his Charisma with the Uncouth flaw and no social skills. Round off with the hacking group at 1 and lots of useless knowledge skills.
Background - an opinionated loser blogger with Asperger's syndrome, whose awakening only fed his superiority complex, but he got caught in an explosion when a gas line ruptured. The company settled with the victims cheaply, and the hospital fixed his extensive injuries with cyberlimbs. Now, the homeless metal mage roams the streets, hoping that a shadowrunning team will take him on as a member. Unfortunately, none will, because he's useless! Even ghouls turn up their noses at him - too much metal, and not enough meaty bits. He lives in fear of a scrap metal dealer who has been chasing him, though.