I checked the Calif EDD web site at http://www.edd.ca.gov/disability/DI_...ime_Worker.htm

It says:

<Reduced Hours

If your work hours must be reduced as the result of a disability, and you suffer a wage loss due to being unable to perform your regular or customary work for at least eight consecutive days, you may be eligible to receive Disability Insurance benefits.

You may receive benefits as long as you have at least $300 in gross wages in your base period, are suffering a loss of wages, and meet other basic eligibility requirements.>

Sounds like you should be able to collect some partial benefits.