Check these bugs:
http://www.google.com/search?num=100&hl=en&c2coff=1&q=%22Error+Applying+Transformations%22&btnG=Search
While they don't appear to directly apply. the information in them may aid in developing a solution. These were the only 2 hits that Google found.
Thanks for the quick reply! :)
Both the bugs there seem to indicate that the problem is with InstallShield. If this were the case, wouldn't more people be having the same issue as me?
One thing I forgot to mention in my first post (actually, I feel really dumb for not mentioning it before now) is that I can install and uninstall JRE 6.0 Update 1 without any issues. This indicates that some part of the JRE 5.0 Updates I have installed currently is corrupted (at least, I think thats what it indicates).