Burned out toroid?! How did you do that? No really, the ferrite is fractured, the copper melted? L
How do you know it's just the toroid which has burned out? Usually, when switch mode power supplies burn out they do so big-time! I'd expect there is other component damage which isn't so obvious as well. Scrap the supply and get another.
Re-design is right. You would have to know the exact specs of the original part to replace it - anything even slightly different from the original can cause damage to the power supply and, more importantly, the super-sensitive equipment connected to it that relies on smooth power with just the right voltage. The bigger question here (if you really want to fix it) is to determine why the toroid burned up in the first place; that sort of thing doesn't just happen. Even if there was a voltage spike on the mains I could name many things that would blow long before the toroid. Just replacing what's burned up is a band-aid. Power supplies are cheap enough in the grand scheme of things. I would, however, recommend getting one rated for more wattage as well as investing in a UPS (Uninterruptible Power Supply, otherwise known as a back-up battery). Aside from the obvious benefit of having some back-up juice in a power outage (which is major if you get caught in the middle of working on something - you don't have to hear thunder for there to be a risk), UPS's are designed to smooth out voltage spikes that could otherwise burn up a computer. Any reputable manufacturer will also provide a maintenance guarantee which pays for the repair or replacement of whatever is connected to it should the UPS fail to protect it.
I wouldn't bother. These things are designed as a unit and replacing a burned out toroid with another one unless exactly the same would muck up the design. If you have another ps that is the exact same design and doesn't work for another reason, you could take the toroid from that one to sub for the other one. Just in case I didn't make it clear before, if you change the toroid for another one that was not designed or it your regulation might be way off and you might end up ruining all your computer parts hooked up to this computer. But on the other hand if it's just a bench power supply - have a go and test what you got.