Do I need a valid passport to renew my green card?
Your Green Card is just a proof that you are allowed to live in US indefinitely. To renew your GC you may or may not require your passport of the country of your origin, as you may provide other identities like your drivers license. However, if you wish to travel outside US your Green Card is useless and you need a passport to obtain visa of the country you wish to visit. Therefore, you must keep your passport of your country of origin always valid.