Blender on the fritz and you can't use it to puree your vegetables? A metal sieve with a wire mesh can come to the rescue.
The video above from the All Nigerian Recipes channel shows the process. You will first need to boil your vegetable for a while. Then put them into the metal sieve and press down so that you get a puree while the skin and other hard bits stay on top. The video, which used tomatoes, says it's best to do this while the tomatoes are still hot. Once you have the puree, put it back on the stove and boil till until the water has dried up.
WonderHowTo tried this trick and says 30 minutes of boiling helped but the tomatoes were still a little difficult to push through, so it might be wise to let them cook for longer if you have the time.
Cooking Hacks: Make Smooth Tomato Puree Without a Blender [All Nigerian Recipes via WonderHowTo]