How can I cook a full chicken with skin on it when my oven is broken?
If you are intent on cooking the bird whole (as opposed to butchering it into pieces which you can fry in a pan), then your only option would be to braise the bird in a large pot, preferably a Dutch oven.  There are myriad recipes online; search for "Chicken in a Pot" or "Braised Whole Chicken".  As ElendilTheTall mentioned in the comments above, the only other option to keep the chicken whole would be to use a barbecue/grill.