Your predicament is unfortunate. You state that your attorney has let deadlines pass in connection with discovery requests. This could lead to problems in your case, as the failure to answer requests for admissions in a timely manner will result in a finding that the requests are deemed admitted. This could mean that the opposing party has evidence that could be lead to the dismissal of your case.
I would recommend that you first of all file a Motion for Continuance in your case and request a hearing, there you can tell the judge what happened with your previous attorney and that you need to retain competent counsel and need time to do it and relief from discovery deadlines. Then you need to go ahead and hire a new attorney to see the case through.
In regard to the potential legal malpractice that was committed by your previous attorney, your claim is not yet ripe. Generally, a party may claim legal malpractice against an attorney that represented the party in litigation
, if there was a failure on the part of the attorney that was not up to the standard of care for attorneys in that situation and it led to you losing the case or not recovering certain damages to which you were entitled. In this case, the attorney's potential malpractice was their failure to work on the case and to answer and conduct discovery. However, there must be finality to the damages caused by the malpractice before you can assert a claim. This means that you actually have to lose the case before your claim for malpractice is ripe. Further, if you don't attempt to win the case, either by prosecuting it yourself or by hiring another attorney, then you could be found to have contributory negligence which might reduce your claim against the attorney.
So, first things first: move for continuance and hire a new attorney. Second thing to do is to file a complaint against the attorney with the State Bar. Depending on what the State Bar finds, the attorney could be punished (or even disbarred) and could be ordered to give you some sort of restitution
Please let me know if this answers your question or if you have need for clarification on any of the points above.
Zachary D. Norris