at first, I had no problem transferring songs in limewire over to i-tunes; now it won't work. have i turned something off, or on, that is stopping me?

Do you mean the LW playlist that appears in iTunes? If yes, then go to LW's menu bar, Tools>Options>iTunes>Sharing & enable option. If still not working, then go to Tools>Options>Sharing & enable Share Finished Downloads.
If you mean adding to iTunes music library, then there's a few techniques as described here How to transfer music to my iPod (& iTunes)

My Library was open in I-tunes, in one window, and my downloaded songs were open in lw in another window; i was able to drag 31 songs from limewire to itunes, then after that, i couldn't any more.

Hmm ... check they aren't the same. iTunes will not allow you to copy to the music library files that have the identical characteristics such as size, name, id3 tag, etc. that are already in the library. Check to see the songs aren't already in there. Check it by band or song alphabetically. I also like to check what songs have been added by arranging by date added in iTunes. Go to edit>view options & enable this. click or double-click top of that column heading to arrange them thus.

As far as share immediately completed downloads, that option is at the bottom of the Sharing options window in LW. But that is really only important if you want the songs to be in the LW playlist in iTunes. To add them to iTunes properly, select saved files folder in library window, press Explore button so the folder opens, then select songs & drag & drop onto library icon in iTunes.

Tell me if I'm not understanding your problem or my suggestions don't fix it.

OK. my LW and IT are both open;
how do I open the "Sharing options window in LW" as you say?

Also, i find that my "henryt's LW tunes" in IT has all 52 songs in it, but only 31 of them are in the Library.

Go to LimeWire's menu bar, Tools -> Options -> Sharing.

The way I like to add songs to iTunes is: go to your LW Library window, select Saved Files folder & press the Explore button. Sample image here: Using Library Explore button to access downld folder (click on link) & the folder will open up for you. Then select all the songs (hold down SHIFT key to select multiple files at once) & drag & drop onto Library icon in iTunes above the playlists.

It might be worth taking the details of one or more of those you are having problems adding & searching your computer. You may find the files are already in the iTunes library but perhaps they don't show where you'd expect them to show because their id3 tags are not read by iTunes as you'd expect.