Part A: Patients receive oblimersen IV continuously on days 1-7. Patients also receive dexrazoxane IV followed by doxorubicin IV over 15 minutes followed by cyclophosphamide IV over 1 hour on days 5 and 6. Filgrastim (G-CSF) is administered subcutaneously once daily beginning on day 8 and continuing until blood counts recover. Treatment repeats every 21 days for up to 18 courses (1 year) in the absence of disease progression or unacceptable toxicity. Patients with stable or responding disease whose shortening fraction falls below 28% by echocardiogram or whose total life-time cumulative anthracycline dose exceeds 750 mg/m^2 may receive additional courses of oblimersen and cyclophosphamide without doxorubicin and dexrazoxane.