I'm sorry but I tried to help earlier but had problems getting in the site. Take a garden hose and feed it into the floor drain. If you can get it through the trap great, if not it will still work. Pack an old wet towel around the hose and floor drain and holding it tight have someone turn the water on. If it's a clog this will usually clear it. If it doesn't it could be roots or a broken tile or fitting. If you have a junk hose that you can cut the male end off of you can usually feed it all the way out to the city main to clean the line. If you have an older home the sewer tile are probably clay and roots can get inside easily. If a newer home with PVC sewer you should be good with a cleaning. Your floor drain is cast iron and the plug is ductile iron and the two usually don't rust together badly. Do what Rob said and PB Blaster it over night.