What's the best way for me to resolve the DUI case I got in California back in 2002?

Best? The only way: To handle the arrest warrant you have, you must turn yourself in to the issuing court, with or without an attorney. On felony charges, the defendant must be personally present at every court hearing and appearance. On misdemeanors and infractions, which I assume this is, an attorney can appear in court without the defendant being present which is safer and avoids immediately being taken into custody. You'll try to negotiate a recall of the warrant[s] and bail reduction or OR release. You'll try to negotiate a plea bargain on any Failure to Appear charge or probation violation that caused the warrant. You'll try to negotiate a plea bargain or take to trial the outstanding charge that caused the warrant. While this isn't a 'capital case', you now face potential jail and fines, so handle it right. Effective plea-bargaining by your attorney, using whatever legal defenses, facts and sympathies there may be, could possibly keep you out of jail/prison, or at least dramatically reduce it, and may enable you to get your probation and programs reinstated. Unless you're competent to effectively represent yourself in court against a professional prosecutor trying to put you in jail, most people hire an attorney who can.

If this was a normal DUI, no injury and no priors, you could hire a CA attorney to try to resolve the case for you. I can't guarantee no jail, there is a minimum of 2 days jail some counties require in the area of 10 days or more depending on the blood alcohol result.

You need to find a lawyer who works in the area your case was filed, they may be able to answer the question. We handle cases throughout Northern California, frequently we are able to get warrants recalled, defend "old" DUI charges and help our clients avoid conviction, or at the very least avoid jail.