If you didn't get the answer on how to fix this, I just did so for our S410. Remove the four screws on the end plate that holds the door hinge in place. The screws are different lengths, with the longer ones on the bump towards the center of the plate, where the wrist strap attaches. Keep the lengths separate. The plate drops off when the last screw is removed, and the door will drop out of the groove. Pull the wire hinge out, taking care not to to loose track of the tiny spring that is near its center. Reverse these steps to put the new door in place. It took some fiddling to get the ends of the spring realigned with the slots that hold them, but I discovered that it worked fine if I held the door in the full open position while reinstalling a screw to hold the plate down.
I nearly lost the spring, and I also found that it isn't much of a problem to have it missing. The door flops open fine without it.
Hope this experience helps you or the next one to need the information.
BTW, I bought the replacement door from digitalcamerapartsdepot.com and got speedy service.
A Canon Elph, July 2005