You can access archived posts even if you're not a subscriber.
Becoming a subscriber gives you the capability to do full-text searches, i.e. search the body of a post rather than just the title.
Regardless of whether you subscribe, you can still find posts by a specific person using the method described above. But as far as I know, threads are stored as threads, not a series of posts, so you wouldn't be able to search for just a specific post in a thread -- you'd retreive the whole thread, not just the post. But, you can find a thread even if the person you're looking for isn't the thread originator (i.e., if you posted in a thread, and you later ran a search on your name, that thread would be returned, even if you didn't start the thread). You would simply have to search through the thread manually to find any specific post. Use your browser's Find (on a page) feature to help you out with this. I could be wrong about this part though -- I'm not a subscriber (but what I described makes sense given what I can tell about the way the forums work).
I hope this all makes sense.
edit: BTW I re-read the this thread again and it seems you might be confused about the Filtering feature in the search function. You only have to enter one thing in the "Main Search Criteria" to have a valid search -- a search phrase (search thread titles), and/or a post author. Select either Current Messages or Archived Messages directly below. Everything under "Filtering" is optional (even though it says 'Select' in the drop-down box, you don't have to select anything) -- if you don't specify a time-frame, all current messages will be searched. Make sure to select at least one Forum Category if you want any results. Selecting a particular one will help you whittle down your search, while clicking 'Select All' will give you a complete listing of posts in all forum categories.