It is not uncommon for United States immigration agents to let a green card holder enter the US with a valid (or even expired) alien registration card even if returning after years without a reentry permit. Be prepared for extensive grilling or even directives to apply for a renewal within a certain period, but do not be shocked if you are denied entry for abandoning your green card and sent back home. The agents at the airport have enormous discretion in such matters and chances are that children or senior citizens or young mothers will be treated kindly while everyone else will be held to a higher standard. In any case, the officer is looking for your ties to the US and is trying to find if you have genuinely abandoned your permanent resident status or if there were compelling reasons to stay overseas for this long, so you better have your story straight along with supporting evidence.
However, if you want drama-free, guaranteed entry, you should have applied for a re-entry permit prior to leaving the US (and that is why it is strongly recommended not to try the path of just showing up at the US border because being denied entry and put on a return flight home is never fun). If you did not, then, your best course of action is to Returning Resident Visa (SB-1). The process is not as comprehensive as the one for green card, but is still convoluted. In addition, you will need to go for an interview and satisfy the consulate officer that you intended to return in time and did not because of reasons beyond your control. Make sure that you have paperwork to support your arguments (e.g. if you claim that you were sick, you better have records of your illness). Do not try this route if you were simply sloppy or lazy or have actually started living abroad and just want the GC to be able to visit the US without a visa, because then your application will be denied and you would have ended up wasting time and money. Instead, apply for a fresh application for permanent residence.