said by MineCoast:
Wow. Interesting. I think really screwed up when I connected the 4 prong I think.
I followed the green wire that is connected to the case and it is connected to the nautral terminal, so I had the ground from the 4 prong cable connected to the nautral which I don't think would have been right.
As long as everything is working as it should, you didn't hurt anything. However the problem with how you had it was that if the neutral should open, instead of the dryer motor stop running, it would use the equipment ground conductor as the neutral. Under the right circumstances, it also could be possible that other household current could use the dryer as a path to ground which is a bad thing.
The band or strap should only be screwed to the frame if you don't have a equipment ground conductor (aka the 4th green wire). With a 3 wire cord, the neutral and equipment ground are the same. It's not as safe as a 4 wire plug with a dedicated equipment ground conductor, but is permitted by code and is normally only a danger if the unit is miswired or a hot touches the dryer frame and there isn't a neutral/ground available to trip the breaker.