Your personal liability for any corporate debts (ie: debts that are co-signed or guaranteed by you as an individual) will be discharged. However, your corporation will still have liability.
You can file bankruptcy on behalf of the corporation, file a formal dissolution, or just allow the corporation to be suspended for nonpayment of annual franchise taxes. The State of California will not allow a corporation to formally dissolve unless either all of the debt is paid prior to dissolution, or someone agrees to assume liability for the debt of the corporation.
Individuals often have nondischargeable personal liability for payroll taxes and sales taxes. Therefore, if at all possible, the taxes should be paid.