My homemade burger patties became smelly after one day kept in the fridge (not the freezer). The taste after I grilled them was also not good. Along with the smell, there is also blood stagnant inside the container.  Are there any solutions? Should I have boiled the beef first? But then I wonder if the taste after I grilled the patty would be different. 
Do you have a fridge thermometer? Confirm that your fridge is below 40°F (~4°C). Preferably around 37°F (~2.5°C), or, if you're primarily storing meat, colder (you can actually go slightly below freezing). If your fridge is too warm, things will spoil much faster.  That said, when meat is ground, all the contaminants on the outside are mixed in. So the shelf life is quite limited. And as you work with it, you'll want to keep it cold (e.g., make sure your marinade is cold when you add it). That said, unless you have a really cold fridge (around 30°F/-1°C gives you another few days), ground meat should only be stored for a day or two. Of course, you can put it in a ziploc bag, and put that in an ice bath in the fridge to get almost that cold.  You should not boil the burgers, that will certainly make it safer, but the taste will be pretty bad. If you have a low-temp (sous vide) setup, you could pasteurize the formed patties at around 57°C, that should be fine. But you don't want to bring them to 100°C, that's certain!  If your marinade contains water, you can get it cold by substituting ice for some of the water (equal amount by weight).  So, my suggestions would be:   check your fridge temperature buy the ground meat (or grind it yourself, whichever) on the day you plan to use it. If you want to marinate for more than a few hours (normally not needed with burgers, but...), make sure the marinade is cold. You need to keep everything below 40°F (4°C). If you really want to push it to keep for more than 2 days, store it in an ice bath in the fridge.   If you have the equipment, you can use low-temperature pasteurization to make it keep much longer. And also to safely serve a medium-rare burger. 