Ok, well this simple information was indeed helpful, for things are starting to make sense. However, I have Windows Vista x86 and I'm thinking this is an "idiosyncraticy" thereof.
I set the class path--set CLASSPATH=C:\program files\java\jdk1.6.0_10\bin, and after moving Helloworld.java to that directory (having had to approve it through Vista's stupid WAC crap), I was actually able to create a .class file of Helloworld. To my surprise, however, it was not placed in that directory folder--it was placed in C:\users\christopher howerter\appdata\virtualstore\java\jdk1.6.0_10\bin!!!
I am pretty sure that this written to an alternate directory is due to the WAC, but I'm not sure (even running the command prompt "as an Administrator" does not rectify this issue)...I believe there is a stigma with writing a file to any directory within the program files directory (or Windows, etc.).
Nevertheless, I tried setting the CLASSPATH to that (what is a "hidden") directory--C:\users\christopher howerter\appdata\virtualstore\java\jdk1.6.0_10\bin, and it set just fine (as would anything, of course). So, I tried typing--java Helloworld--while in the C:\program files\java\jdk1.6.0_10\bin directory) and received a slew of errors, as it won't actually let me access this hidden directory in which the .class file exists through the command prompt (as it "does not exist," see above).
Then, I tried resetting the CLASSPATH to C:\program files\java\jdk1.6.0_10\bin, and just moved the created .class file from the hidden directory to that one (where the .java file exists, of course, as I moved it there--see above). I tried yet again running it and got the same list of errors:
Exception in thread "main" java.lang.NoClassDefFoundErorr: Helloworld
Caused by: java.lang.ClassNotFoundException: Helloworld
at java.security.AccessController.doPriviledged(Native Method)
Could not find the main class: Helloworld. Program will exit.
All I can say is that I hope all of that error code typing was not in vain (since one can't copy from the command prompt, at least to the best of my knowledge, which isn't very great...)! I was never taught how to diagnose these sorts of errors--only to double and triple check the code! However, who could screw up Helloworld?--rhetorical question, I assure you.
BTW, after trying to help me some more, as a side question, where can you find resources to try and solve huge strings of errors like that? I know they can often be caused by one typo and fixed at the snap of a finger, but for something like this.