Will I have any problems obtaining a new CA driver's license with a record of one DUI in 2004 in the state of WA? Are there any restrictions or time limits?
As long as you had your WA license reinstated following any suspension or revocation, you should be fine. In WA, if you were suspended or revoked due to the DUI, you would have been required to carry SR22 insurance for 3 years. Assuming that requirement has been complied with and your WA license has been reinstated, you should have no problem being licensed in most states. If you are not sure about the status of your WA license or driving privilege, you can check it at dol.wa.gov.
The existence of a prior conviction of this age should not interfere with your obtaining an unrestricted California license. You should be aware that California considers priors for up to ten years in the event that you received another driving under the influence in California.