How to unjam lens zoom?

I think I've done something similar on the Minolta/Sony "A mount" Sigmas, so this may or may not work. On the Minolta variants, the trick that often works is to use a flathead to "unstick" the gears if it's minor. If it's more severe, you may need to remove the lens mount from the lens, then move it around to loosen it. On Cannon EF lenses, you need to put it in MF mode and move it around or take the lens apart to adjust it (and remove the AF/MF switch so it moves the AF gears around). If it sticks on a Canon, you HAVE to take the lens apart.

If neither of those tricks work, you need to remove the lens body and check the gearing inside. Be careful not to adjust the front element in error as the body locks the adjustment in place on old Sigmas, unless you know how to re-adjust it!

However if in doubt, have a shop do the repair. Once you get the adjustment wrong, you will not get it back easily unless you know how. If I was working on a Sigma 35mm Canon EF, I'd want to keep it where it is but also have my T3 test dSLR ready to check it. The crop factor may make it harder, but 5D's are too expensive to consider "tester" bodies; non-i bodies are cheap.