These cameras are more durable then most think. I just put it in my backback wrapped up in an insulation layer (sweater).
The lens is Canon's top of the line gear. It's made to be thrown around, dropped, etc. The camera, an Xti, is relatively cheap in comparison, but I've owned 3 Canon cameras and abused all three and they all work perfect still. Always bring them snowboarding, mountain biking, and dirt biking. I even dropped this camera in the snow this weekend without a lens on. Cleaned the mirror to the best of my ability and I think the pictures are still perfect! haha. It was wet on the outside for a few minutes too.
Try recharging your battery. I know mine freezes when the battery is low.
My only worry about tunnel bags is the heat and moisture given off by the melting snow on the tunnel. Also, it would see a lot more vibration then on the rider. I fall off the sled and don't even think about it though. My biggest worry is the connection between the camera and the lens. I think I should probably take them apart next time.
What type of camera did you use that isn't working now?
I have a Canon EOS Rebel. It must be an early version since there's no XT or XTi labels. I've only used it once sledding with the 18-55mm lens. Depending on whether this can be fixed will help me decide in upgrading the lens. I've tried recharging both batteries with no luck so I think I'll need to take it in to a service centre.