Got a DWS ticket (NJ in 2006. I moved to CA before my court date. Judge issued FTA warrant & set bail @ $5k. I cannot get my CA DL. What can I do?

You are going to have to clear things up back in New Jersey first.  You will need an attorney there to help.  Frankly, your license might be the least of your problems.  A bench warrant for your arrest has been issued.  Warrants don't expire.  While the authorities won't actively pursue you for something like this, if you are stopped by the police for any minor infraction, even jay walking, you can be taken into custody.  At the very least this can all come up on an employment background check.

Again, hire an attorney licensed in New Jersey and who practices locally in the area where the warrant was issued; they can best utilize their contacts to your fullest advantage.  And plan on a trip to the Garden State.