I'm using Internet Explorer with no problem. I don't know which version I'm on since my laptop is at home and I'm at work now. But it should be the latest that is automatically updated by the Microsoft update software.
I noticed that the puzzle software changed a bit several weeks ago, and maybe that's when the incompatibility with your system started. It used to be that you had a moveable menu in the upper-left corner of the puzzle area that could get in the way of the pieces. All of that functionality has been moved to below the puzzle area. Also, the software now keeps track of what you have done in the past so if you open a puzzle that you completed before, you will now see it in its completed state. The changes themselves aren't important to you, but the fact that they changed might be.
Also, it looks like our puzzles are actually run by Jigsaw Planet (
http://www.jigsawplanet.com/. At least, the software looks the same. You might want to go there directly and see if their other puzzles work for your system.