Alright, when I click update, it just jumps to the "Update engine and virus definitions" button and runs it automatically, then comes with the same results as before.
I then skipped to trying the repair option under Add/Delete in Control Panel, which told me there was some kind of error with some files (didn't think to write which ones down, but I believe they were database files) and to use the full update option instead, so I pulled it up again and instead chose "Update" instead of "Repair." It seemed to download some files, but when I looked, the same was still displayed.
However, when I went and manually downloaded the file from your second suggestion and ran it, it told me that it successfully updated from 120412-1 to 120413-0. Even though the avast! was telling me that I had 120306-0 before hand. When I looked in avast again afterward, it was showing 120413-0. So it is correct now, and thank you.
I guess it seems that it was updating properly, but not changing my definition version number in avast! for some reason. Hopefully everything is alright now, but I won't really know until the next definitions update.
Again, thank you for the help on the problem.