Analysis is the same function whether you run it manually from the selection at the top of the window in Shrink or from the Quality Settings tab once you hit Backup. (run your cursor over the Analysis icon and you'll see it says Deep Analysis).
Analysis examines the movie frame by frame to determine where compression can be applied most effectively without adversely affecting the visual quality. This works up to a point. Shrink will try to apply compression to B frames first, but if the compression is beyond what can be obtained working solely with B frames, it will move on to I and P frames, which leads to more severe artifacts showing up in the video. Without running Analysis first, Shrink has to determine the correct frames to compress on the fly. This is why you should always run Analysis (from either spot) when using Shrink.
It does have an effect on the way Shrink operates, so there is a possibility that it will help in durkinjt's problem, but I still think it is a long shot and there is something gone wrong in the way the program is set up within the operating system.