As you are probably aware, "screwed" and the stronger "f" word (and their variations) have many many meanings that are very context sensitive.
In this case the context indicates that the lawyer is in a difficult position. Perhaps he fears losing his trial case, or he has given very bad advice to a client and cannot correct the problem easily.
By using the word "still" in the sentence, it indicates that he has tried to solve this problem but his attempt failed. The lawyer in saying that he is screwed indicates that he sees no solution to his dilemma and he faces a major disaster.
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